; or using a terminology well known from acoustics, there appear overtones in the motion of the hydrogen atom.
Another simple example of the application of the correspondence principle is afforded by a central motion, to the investigation of which the explanation of the series spectra in the first approximation may be reduced. Referring once more to the figure of the sodium spectrum, we see that the black arrows, which correspond to the spectral lines appearing under the usual conditions of excitation, only connect pairs of points in consecutive rows. Now it is found that this remarkable limitation of the occurrence of combinations between spectral terms may quite naturally be explained by an investigation of the harmonic components into which a central motion can be resolved. It can readily be shown that such a motion can be decomposed into two series of harmonic components, whose frequencies can be expressed by
and
respectively, where
is a whole number,
