1921-22.] Quantum Theory of Secondary Spectra. 
247. 
XVII.— The Quantum Theory of the Secondary Spectrum of 
Hydrogen. By John Marshall, M.A., D.Sc., University 
College, Swansea. 
(MS. received March 18, 1922. Read May 15, 1922.) 
Introduction. 
It is proposed in this paper to consider the spectral lines which would 
arise in the case of an electron describing an orbit about two centres of 
attracting force. The assumptions of the Quantum Theory as generalised 
by Wilson and Sommerfeld are made. The centres of attracting force 
are assumed, as in the simpler applications of the Quantum Theory, 
to be at rest. Such a spectrum would arise in the case of a hydrogen 
molecule which had lost one electron and in which the remaining 
electron described an orbit about the positive nuclei. Novikoff has shown 
that this configuration would be stable {vide Whittaker’s Analytical 
Dynamics, 2nd ed., p. 407, ex. 1). It follows that, if at any stage an 
electron were withdrawn from a molecule, the remaining electron would 
describe a stable orbit. Much experimental work has been done on 
the secondary spectrum of hydrogen, but I am not aware that any 
theoretical explanation has been given of the immense number of lines 
found by experiment. Dufour in Ann. de Chimie et de Physique, 1906, 
gives a very complete account of the work done on this spectrum and 
the various controversies which it has evoked. Dufour’s conclusion is 
that the spectrum of the atom is the primary spectrum, and that the 
secondary spectrum is due to the molecule. H. E. Watson in Proc. Roy. 
Soc., vol. Ixxxii, 1909, states the main points at issue, and gives the most 
modern measurements of the lines and compares his results with wave- 
lengths found by Hasselberg {Mem. Acad. Imp. St Petersburg, vol. xxxi, 
1883), Ames {Phil. Mag., vol. xxx, 1890), and {A strophysical Journal, 
vol. xvi, 1902). 
Buisson and Fabry {Journal de Physique, vol. ii, p. 442, 1912) have 
measured with an interferometer the widths of the spectrum lines, and 
have referred at least a part of the lines of the secondary spectrum to 
the hydrogen atom. The complications which are introduced into the 
theoretical investigations, however, seem to indicate that the explanation 
of the lines is to be sought by the application of the Quantum Theory to 
molecular orbits. 
