The possible necessity for an alteration of this kind in assumption C may perhaps not seem unlikely when it is remembered that the laws of mechanics are only known to hold for certain mean values of the motion of the electrons. In this connexion it should also be remarked that when considering periodic orbits only mean values are essential (comp. I. p. 7). The preliminary and tentative character of the formulation of the general assumptions cannot be too strongly emphasized, and admittedly they are made to suit certain simple applications. For example, it has been already shown in paper IV. that the assumption B needs modification in order to account for the effect of a magnetic field on spectral lines. In the following sections some of the recent experimental evidence on line spectra and characteristic Röntgen rays will be considered, and I shall endeavour to show that it seems to give strong support to the main principles of the theory.
§ 2. Spectra emitted from systems containing only one electron.
In the former papers it was shown that the general assumptions led to the following formula for the spectrum emitted by an electron rotating round a positive nucleus
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