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IjI V. The Helium-Hydrogen Series Constants. 

 By Herbert Bell *. 



AS is well known, Bohr proposed to modify the Bulmer 

 formula for these series by a term depending on the 

 relativity-effect on the moving electron f. The formula for 



Helium thus becomes 



-'M^K— (>,:=>}• • « 



where p and m are integers, m>p, NHe=lM He /(Mj Te + / u,), 

 1\ being Rydberg's constant 2tt' x 'e 4 fx\rlr ! , Mh ( . the mass of the 

 helium atom and /j, that of the electron, while a— 'lire 2 [he. 



The Helium lines, however, display a fine-structure under 

 high resolving power, and Sommerfeld % in explanation of 

 i his developed a theory of adjacent (elliptical) orbits with 

 eccentricities depending on quantum considerations. He 

 gives a a physical meaning as the ratio of angular momenta, 

 and proposes to measure it from fine-structure observations. 

 We know from other considerations that a 2 has approxi- 

 mately the valuef5'3x 10~ 5 . 



Paschen § tested this theory by an exhaustive set of 

 measurements in the helium spectrum and substantial 

 verification was apparently obtained. His value for a 2 from 

 the line U\8€> is 5*315 x 10~ 5 . 



According to Sommerfeld's theory the series (1) when 

 p = 3, m = 4, 5, . . . , which is the one most easily re- 

 solved, consists of a set of triplets having components I, 

 II, III, in diminishing order of wave-length, their wave- 

 number differences being constant. 111 — 11 = 1*73 cm. -1 , 

 IT — T = * 5 8 cm. -1 . Further, each component is bordered 

 towards the red by a set of fainter lines rapidly closing in 

 on them as higher terms of the series are reached. 



Formula (1) is to apply only to I, and can therefore 

 be accurately tested. Paschen of course did this, implicitly, 

 but the new table from the Bureau of Standards || for the 

 refractive index of air slightly alters his derived constants. 

 His measurements are given in Table I., along with the 

 new additive correction to reduce to vacuum, the figures 

 in italics referring to the series p = 4, m = — , 6, 7, .... the 

 others to £> = 3, m = 4, 5, .... 



* Communicated by the Author, 

 t Phil. Mag-. Feb. 1915. 

 t Ann. d. Physik, li. No. 17 (1916). 

 § Ann. d. Physik, 1. No. 16 (1916). 



>| Bureau of Standards. Washington, ' Scientific Papers,' No. 327 

 (1918). 



Phil. Mag. S. 6. Vol. -40. No. 238. Oct. 1920 2 K 



