﻿334 Series Spectrum of Hydrogen and Structure of Atom. 



is not neglected, Dr. Allen's formula will show a deviation 

 from the Balmer law which is much larger than that observed 

 by Mr. Curtis, and which has the opposite sign. It therefore 

 seems to me that the interesting suggestion of the nuclear 

 magnet and the calculation of its moment can hardly be 

 considered as supported by the experiments of Mr. Curtis. 



I should like here to draw attention to an effect of 

 another kind, which involves a correction in the theoretical 

 formulae for the hydrogen spectrum, i. e. the variation of 

 the mass of the electron with velocity. It seems necessary 

 to take this into account even if other effects may be in- 

 volved at the same time. Assuming that the orbit of the 

 ♦electron is circular, and proceeding in exactly the same way 

 as that followed in the deduction of the Balmer formula on 

 the quantum theory, but replacing the expressions for the 

 energy and the momentum of the electron by those deduced 

 on the theory of relativity, we obtain the following formula 

 for the hydrogen spectrum : 



_ 27rVmM /l 1 \ r ttV / 1 1 Y\ 

 V ~ ft»(m+M) I n/ n£ ) [_ ^ Ui 2 ~ + n*VJ ' 



where e and m are the charge and the mass of the electron, 

 M the mass of the nucleus, A Planck's constant, and c the 

 velocity of light. In the formula, terms are neglected which 

 involve higher power than the second of the ratio between 

 the velocity of the electron and the velocity of light. The 

 correction due to the last factor in this formula has the same 

 sign as the deviations from the Balmer iaw observed by 

 Mr. Curtis *. However, it accounts only for X of the 

 deviations observed. 



In connexion with this discussion it may be remarked that 

 it seems hardly justifiable to compare the measurement of 

 Mr. Curtis with any theoretical formula unless the observed 

 doubling of the hydrogen lines is taken into account. Con- 

 sidering that the distance between the components is much 

 greater than the deviations from the Balmer law and that 

 the components are of unequal intensit}-, it is difficult to 

 know, in the absence of a theoretical explanation of the 

 doubling, the interpretation to be placed on measurements 

 of the " centre of gravity " of the lines. In a previous 

 paper I suggested that possibly the lines were not true 

 doublets, but that the doubling observed was produced by 

 the electric held in the discharge. As Mr. Curtis points 

 out, this suggestion does not seem consistent with the 



* In the diagram in Mr. Curtis's paper (he. cit. p. 615) the curve 

 corresponding to an expression of the above type is inadvertent] v drawn 

 with its curvature downwards instead of upwards. 



