In the present state of the theory it is not possible to account in detail for the formula (13), but it was pointed out in my previous papers that a simple interpretation can be given of the fact that in every series
approaches unity for large values of
. It was assumed that in the stationary states corresponding to such values of
, one of the electrons in the atom moves at a distance from the nucleus large compared with the distance of the other electrons. If the atom is neutral, the outer electron will be subject to very nearly the same forces as the electron in the hydrogen atom, and the formula (13) indicates the presence of a number of series of stationary states of the atom in which the configuration of the inner electrons is very nearly the same for all states in one series, while the configuration of the outer electron changes from state to state in the series approximately in the same way as the electron in the hydrogen atom. From the considerations in the former sections it will therefore appear that the frequency calculated from the relations (1) and (13) for the radiation emitted during the transition between successive stationary states within each series will approach that to be expected on ordinary electrodynamics in the region of slow vibrations[18].
From (13) it follows that for high values of
the configuration of the inner electrons possesses the same energy in all the series of stationary states corresponding to the same spectrum (11). The different series of stationary states must therefore correspond to different types of orbits of the outer electron, involving different relations between energy and frequency. In order to fix our ideas, let us for a moment consider the helium atom. This atom contains only two electrons, and in the previous papers it was assumed that in the normal state of the atom the electrons rotate in a circular ring round a nucleus. Now the helium spectrum contains two complete systems of series given by formulæ of the type (11) and the measurements of Rau mentioned below indicate that the configuration of the inner electron in the two corresponding systems of stationary states possesses the same energy. A simple assumption is therefore that in one of the two systems the orbit of the electron is circular and in the other very flat. For high values of