1916] on The Spectra of Hydrogen and Helium 653 



emitted when only one of the electrons is regained by the nucleus. 

 [n a first approximation, the general formula is identical with that 

 for hydrogen, except that the Rydberg constant has four times its 

 ordinary value. This formula gives lines coinciding in position with 

 the Principal series calculated for hydrogen by Rydberg, and also 

 with those of the supposed second Principal series/and unites them 

 in a single series of a new type. Not only this, a subsequent correc- 

 tion of the formula, no longer regarding the mass of the electron as 

 negligible in comparison with that of the nucleus, accounted exactly 

 for the slight differences between the positions of the lines 4086, etc., 

 calculated by Rydberg and those in w^hich they had been observed. 

 Thus, according to Bohr's theory, the new helium-tube lines were to 

 be attributed to a simplified form of helium and not of hydrogen. 

 For the sake of distinction, we may conveniently follow Lockyer's 

 notation and refer to the new spectrum as that of " proto-helium." 

 Bohr's results may then be expressed as follows : — 



Hydrogen — 



, , ^ s [p = ^) for infra-red series. 



?i = N (— 2 - — J -j/? = 2 for Balmer series. 



\p- m / [p = I for extreme ultra-violet series. 



Proto-helium — 



„ _ xri/ 1 _ ^ \ (/? = 4 for Pickering series. 

 \f 7n:') \p = 3 for ^' 4686 "^series. 



In the first approximation N^ = 4 N, but taking account of the 

 mass of the electron, the theoretical expressions for N and N^ are 



N = 



ch^ (M + m) 



^1 ^ 27r^(2E)^e^(4M)??2 

 c^3(4M + m) 



where E, M = charge and mass of nucleus of hydrogen atom ; 

 e, m = charge and mass of electron ; c = velocity of light ; and 

 h = Planck's constant. Using the best available determinations of 

 these quantities, the resulting value for X in the formula for hydrogen 

 is as near to 109^675 as can at present be expected. The ratio of 

 N^ to X can be determined precisely from the formulae, as the 

 more doubtful quantities cancel ; taking M/w = 1835, we find X^ 

 = 4*001632 X, in remarkable agreement with the value determined 

 from the actual spectra. Assuming the truth of the theory, the 

 spectroscopic data thus provide a valuable check on the generally 

 adopted value for the mass of the electron. 



Experimental support for Bohr's interpretation of the 4686 series 



