85 



The second coliiinn contains the symbols i/i,,/;.; 11' ■n\,n..\ u") char;icler- 

 ising the transitions between two stationary states of the perturbed system which 

 contribute to the new components. For each component the transitions which give 

 rise to radiation polarised parallel to the direction of the electric force and 

 those giving rise to radiation polarised perpendicular to this direction are collected 

 in brackets and indicated by Par. and Perp. respectively. According to what has 

 been said on page 77, only such slates are taken into account for which 11 is diffe- 

 rent from zero. 



The third and fourth columns contain the values of the squares of the relative 

 amplitudes of the vibrations of frequencies {n\ — n^)(a^ ^ { n], — n' — — n") to., 

 f-(n' — n")w3 in the initial states and final states respectively, calculated by means 

 of (125), (126) and (127). For the original comj)onents these columns contain the 

 values of the squares of the quantities R' and R" appearing in tables IX and X. 



The fifth and sixth columns contain the sums of these squares corresponding 

 to each of the new components respectively, the quantities corresponding to radia- 

 tion polarised parallel and to radiation polarised perpendicular to the axis being 

 taken together respectively. For the original components these columtis contain 

 the values of '- Mi'^R"- and - : n^/î"-. 



The seventh column contains the values of the wave lengths for the différent 

 components. These values may be calculated from the expression (119i for the 

 frequencies of these components and are taken from Paschkn's often mentioned 

 paper. 



We will now proceed to discuss the observations on the fine structure of the 

 hydrogen lines {N = 1) and of the analogous helium lines [N = 2) in detail, and 

 we shall first consider the latter lines for which we may compare with the detailed 

 results of Paschen s observations. Especially in case of two of these lines, viz. 

 4686 Å (4^3) and 3203 Å (5 -^3), Paschp:n has been able to obtain in detail a con- 

 firmation of Sommerfeld's theory regarding the frequencies of the fine structure 

 components, and just for these lines a theoretical interpretation of the observed 

 intensities seems only possible if the effect of a perturbing electric field is taken 

 into account. 



Let us first consider Ihe helium lino 4()86 A (4^3) for which llic observed 

 fine structure exhibits the richest details and therefore ofTers the best op|)orfunily 

 for a comparison with the theory. In fig. 10 on Plate IV a scheme is given of 

 Ihe theoretical and of the empirical results regarding the fine structure of this 

 line. In the theoretical scheme the original components are indicated hy drawn 

 lines and the new components by dotted lines. The lengths of the lalter lines arc 

 for each component taken proportional to tlie sum of the corresponding cpian- 

 tities .s( /?'■-) and s (/?"-) appearing in Table XI. while those of the former lines are 

 taken proportional to twice the sum of the quantities - : n^R'- and - :\ n^R"- appearing 

 in this table. The intensities of the new components, as given in the figure, would 

 correspond to an intensity of 600 Volt cM. In this connection it may be noted. 



