the difference in energy between two different stationary states of the system. Since we have seen in [§2] that a configuration consisting of two nuclei and a single electron rotating round the line between them is unstable, we may assume that the removing of one of the electrons will lead to the breaking up of the molecule into a single nucleus and a hydrogen atom. If we consider the latter state as one of the stationary states in question we get
The value for the frequency of the ultra-violet absorption line in hydrogen calculated from experiments on dispersion is
.[44] Further, a calculation from such experiments based on Drude’s theory gives a value near two for the number of electrons in a hydrogen molecule. The latter result might have connexion with the fact that the frequencies calculated above for the radiation absorbed corresponding to vibrations parallel and perpendicular to the plane of the ring are nearly equal. As mentioned in [Part II.], the number of electrons in a helium atom calculated from experiments on dispersion is only about ⅔ of the number of electrons to be expected in the atom, viz. two. For a helium atom, as for a hydrogen molecule, the frequency determined by the relation
agrees closely with the frequency observed from dispersion; in the helium system, however, the frequency corresponding to vibrations perpendicular to the plane of the ring is more than three times as great as the frequency in question, and consequently of negligible influence on the dispersion.
In order to determine the frequency of vibration of the system corresponding to displacement of the nuclei relative to each other, let us consider a configuration in which the radius of the ring is equal to
