## Extract

The purpose of the present paper is to apply the quantum theory of spectrum emission by atomic systems containing an *aspherical* nucleus, given in my recent paper, to the Balmer series of hydrogen. Although, in working out the general formulæ of the said theory, I have had in view chiefly the more complicated, non-hydrogenic, spectra as a possible field of its application, yet it has seemed worth while to compare also the aspherical nucleus formulæ with the Balmer spectrum of hydrogen, the more so, as recent measurements have revealed a notable deviation of at least the first six members of this series from the simple Balmer formula. The measurements alluded to were made by W. E. Curtis in 1914, and their newly revised results are tabulated in his paper of 1919, for a copy of which accompanied by helpful explanations, I am indebted to Prof. Fowler. 1. It will be sufficiently general for the purpose in hand to assume an *axially symmetrical* nucleus of unknown asphericity (to be determined from the observations). Then the series will be given by the formulæ (28), (28·1), with *k* = 1 (*i. e.*, nucleus charge = *e*), with *n'* = 2 written for the constant term, and *n* = 3, 4, 5, etc., for the members H_{α}, H_{β}, H_{γ}, etc., of the series. Thus, if N be the Bohr value of the Rydberg constant, and if (retaining all other symbols of my quoted paper) we write for brevity σ = (2N*ch*/*e*^{2})^{2}. (A - B), (1) the frequency formula will be *v* = N/4 {1 + 4σ*g'*/(2 - *n'*_{3})^{6}} - N/*n*^{2} {1 + *n*^{2}σ*g*/(*n* - *n*_{3})^{6}}, (2) where *g* = *g* (*i, ϵ*) for the initial, and *g'* for the final orbit, are as on p. 55 (*loc. cit.*). It will be kept in mind that A — B, and, therefore, σ, may be either positive or negative, according as the nucleus is “oblate” or “prolate” in the generalised sense of these words, as explained in the quoted paper. The variable number *n* is the sum of the three independent integers n_{1}, n_{2}, n_{3}, introduced through the quantum integrals, and, similarly, *n'* = *n*_{1}' + *n*_{2}' + *n*_{3}', the quantised eccentricity *ϵ* and inclination *i* of the electronic orbits, appearing in *g*(*i', ϵ*), being given by (21·3), *loc. cit*.

## Footnotes

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- Received April 16, 1920.

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