[39] See A. S. Russell, Chem. News, cvii. p. 49 (1913); G. V. Hevesy, Phys. Zeitschr. xiv. p. 49 (1913); K. Fajans, Phys. Zeitschr. xiv. pp. 131 & 136 (1913): Verh. d. deutsch. Phys. Ges. xv. p. 240 (1913); F. Soddy, Chem. News, cvii. p. 97 (1913).
[40] E. Rutherford, Phil. Mag. xxiv. pp. 453 & 893 (1912).
Part III.—SYSTEMS CONTAINING SEVERAL NUCLEI [41] [42].
ACCORDING to Rutherford's theory of the structure of atoms, the difference between an atom of an element and a molecule of a chemical combination is that the first consists of a cluster of electrons surrounding a single positive nucleus of exceedingly small dimensions and of a mass great in comparison with that of the electrons, while the latter contains at least two nuclei at distances from each other comparable with the distances apart of the electrons in the surrounding cluster.
The leading idea used in the former papers was that the atoms were formed through the successive binding by the nucleus of a number of electrons initially nearly at rest.
Such a conception, however, cannot be utilized in considering the formation of a system containing more than a single nucleus; for in the latter case there will be nothing to keep the nuclei together during the binding of the electrons. In this connexion it may be noticed that while a single nucleus carrying a large positive charge is able to bind a small number of electrons, on the contrary, two nuclei highly charged obviously cannot be kept together by the help of a few electrons. We must therefore assume that configurations containing several nuclei are formed by the interaction of systems—each containing a single nucleus—which already have bound a number of electrons.
[§2] deals with the configuration and stability of a system already formed. We shall consider only the simple case of a system consisting of two nuclei and of a ring of electrons rotating round the line connecting them; the result of the calculation, however, gives indication of what configurations are to be expected in more complicated cases. As in the former papers, we shall assume that the conditions of equilibrium can be deduced by help of the ordinary mechanics. In determining the absolute dimensions and the stability of the systems, however, we shall use the main hypothesis of [Part I.] According to this, the angular momentum of every electron round the centre of its orbit is equal to a universal value
where