the inner electron in the two configurations will act on the outer electron very nearly as a ring of uniformly distributed charge with the nucleus in the centre or as a line charge extending from the nucleus, respectively. In both cases several different types of orbit for the outer electron present themselves, for instance, circular orbits perpendicular to the axis of the system or very flat orbits parallel to this axis. The different configurations of the inner electrons might be due to different ways of removing the electron from the neutral atom: thus, if it is removed by impact perpendicular to the plane of the ring, we might expect the orbit of the remaining electron to be circular, if it is removed by an impact in the plane of the ring we might expect the orbit to be flat. Such considerations may offer a simple explanation of the fact that in contrast with the helium spectrum the lithium spectrum contains only one system of series of the type (11). The neutral lithium atom contains three electrons, and according to the configuration proposed in paper II. the two electrons move in an inner ring and the other electron in an outer orbit; for such a configuration we should expect that the mode of removal of the outer electron would be of no influence on the configuration of the inner electrons. It is unnecessary to point out the hypothetical nature of these considerations, but the intention is only to show that it does not seem impossible to obtain simple interpretations of the spectra observed on the general principles of the theory. However, in a quantitative comparison with the measurements we meet with the difficulties mentioned in the [first section] of applying assumptions analogous with
and
to systems for which ordinary mechanics do not lead to periodic orbits.
The above interpretation of the formulæ (11) and (12) has recently obtained very strong support by Fowler’s work on series of enhanced lines on spark spectra[19]. Fowler showed that the frequency of the lines in these spectra, as of the lines in the ordinary spectra, can be represented by the formula (11). The only difference is that the Rydberg constant
in (12) is replaced by a constant
