358 



74 



The sixth and seventh columns conlain the values of h.,R'^ and n.,R"-, which 

 may be expected to afîord an estimate for the intensities. 



The eighth column contains the theoretical values for the wave lengths of the 

 components calculated by means of the formulae (119), (120), (121), (122) and are 

 taken from Paschen's paper. 



When discussing the estimate afforded by the preceding tables, it will first of 

 all be remarked that the values of n'^/?'-' and n.^R"- for transitions for which lu 

 decreases by 1 are much larger than for transitions for which n., increases by 1, 

 so that the components corresponding to the former transitions must be expected 

 to be much stronger than those corresponding to the latter. (In § 6 we have already 

 met with the analogous circumstance in the Stark effect, where components for which 

 one of the r's is negative are much weaker than the other components, and the 

 connection was pointed out with Sommkrfeld's suggestion that no transitions would 

 be possible for which one or more of the n's increase. See page 58). It must therefore 

 be expected that in general the line structure of a line {n' ^ n") will consist of n" 

 strong components, corresponding to the transitions 



(n' — n"— 1, 1 - , n" ) 

 ( n' — n" , n" ^ 1 , n"~ 1) 



( n' — 2 , 2 ^ n"— 1 , 1 ), 

 and of n" 1 weak components, corresponding to the transitions 



(n' — n" -\- 1 , n"— 1 • , /?" ) 

 (/J' — /J" + 2 , n"— 2 1 , /» "— 1) 



( n' — 1 , 1 - n" — 2 , 2 ). 



Moreover the values of n[^R'^ and in the tables indicate that the values of 



the intensities of the strong components, to begin with the second, will form a 

 series of decreasing numbers. As to the intensity of the first component we must 

 distinguish between two cases, viz. n' — n" == 1 and n' — n" > 1. In the first case we 

 have to do with a transition between two circular orbits for which n\R'- and n'!,R "' 

 become equal to and n" respectively, and we should expect that the corresponding 

 component would be the strongest of the fine structure under consideration. In the 

 second case the orbit of the electron is circular only in the final state, and R" 

 becomes equal to zero, so that the intensity of the first component in this case 

 must be expected to be less than that of the second. At the same time, however, 

 we should anticipate, from analogy with what has been observed in the discussion 

 of the Stark eiïect in the case of transitions in which circular orbits of the electron 

 are implied, that such conclusions about the intensity of the first component in 

 question will bear a more or less exaggerated character. 



