If the charge on the nucleus and the number of electrons in the different rings is known, the condition in regard to the angular momentum of the electrons will, as shown in [§2], completely determine the configuration of the system, i. e., the frequency of revolution and the linear dimensions of the rings. Corresponding to different distributions of the electrons in the rings, however, there will, in general, be more than one configuration which will satisfy the condition of the angular momentum together with the condition of stability.
In [§3] and [§4] it will be shown that, on the general view of the formation of the atoms, we are led to indications of the arrangement of the electrons in the rings which are consistent with those suggested by the chemical properties of the corresponding element.
In [§5] it will be shown that it is possible from the theory to calculate the minimum velocity of cathode rays necessary to produce the characteristic Röntgen radiation from the element, and that this is in approximate agreement with the experimental values.
In §6 the phenomena of radioactivity will be briefly considered in relation to the theory.
[§2. Configuration and Stability of the Systems.]
Let us consider an electron of charge
and mass
which moves in a circular orbit of radius