Unsymmetrical Components in the Stark Effect. 949 



where N'(m) and N'(?i) are identical functions of m and n 

 respectively. 



§ 4. Application to the H a line. 



We proceed to apply equation (25) to specific lines of the 

 elements. Let us take as an example the H a line of the 

 Balmer Series. Here « 1 + ?? 2 H-w 3 = 2, m 1 -\-m 2 + m 3 — 3, 



v=4-571xl0 14 , \- 

 in the form 



>5628 x 10- 4 ; let us also write (25) 



then 



Av = (P, - QO x K X F + (Q 2 - F 2 ) K 2 F 2 ; 



(26) 



P 1 = (n 2 —n 1 )(n 1 + n 2 + n 3 ), Q, = (m 2 — m 1 )(m l + w 2 +m3),1 

 K - 3A - 



P 2 =(w 1 + n 2 + rt 3 ) 4 O s - %) 2 + (»i + "2 + ^^W, \ (27) 



Q2 = (™i + m 2 + m 3 )%?n 2 - ?nj) 2 + (mj + ??i 2 4- ??i 3 ) 3 N( m) , 



27/t 5 J 



J 



K 9 = 



5127r s E 4 m V 



Then writing down in a tabular form the possible values 

 of n^n^n^ and m 1 ??i 2 m 3 , we have, on availing ourselves of 

 Sommerfeld^s " Auswahlprinzip " for the definition of the 

 plane of polarization and the restrictions on the possible 

 combinations of the quantum numbers : 



Table A. 





n 3 . 



ri 2 . 



n x . 



P, 



P 2 . 



a. 



m 3 . 



m 2 . 



m x . 



Qi. 



Q 2 . 



I. 



2 















128 



3 















1458 



II. 



1 



1 







2 



144 



b. 



2 



1 







3 



2025 



III. 



1 







1 



—2 



144 



c. 



2 







1 



-3 



2025 



IV. 



V. 



\ VI. 



Q 

 







1 



2 

 



1 

 

 2 







4 

 -4 



192 

 64 

 64 



d. 



e. 



1 

 1 



1 



1 



2 

 



1 

 



2 







6 



-6 



2106 

 1458 

 1458 



\ g. 







2 



1 



3 



2025 















h, 







1 



2 



-3 



2025 















i. 







3 







9 



729 















• 











3 



-9 



729 



