not continuously, but by definite steps, as would inevitably be the case if the energy were atomic in structure. I have introduced this illustration from the vortex atom theory of matter, for the purpose of showing that when we have a structure as fine as that of atoms we may, without any alteration in the laws of dynamics, get discontinuities in various dynamical quantities, which will give them the atomic quality. In some cases it may be that the most important effect of the fineness of the atomic structure will be the production of this atomic quality in some dynamical quantity such as the kinetic energy. If then we postulate the existence of this property for the energy, it may serve as the equivalent of a detailed consideration of this structure itself. Thus, for many purposes (for example, in the elucidation of the remarkable results obtained by Professor Nernst and his pupils on specific heats at low temperatures, or Mr. Bohr's researches on the distribution of lines in various spectra) Planck's quantum theory serves as the equivalent of a knowledge of the structure of the atom.
If we assume that the recognized laws of electrical action hold for the small charges carried by the electrified parts of the atom—the electrons and the corresponding positive charges—we can by the aid of mathematical analysis get some idea of the way in which a number of electrons will arrange themselves when in stable equilibrium. We find that in a symmetrical atom only a limited number of such electrons can be in equilibrium when arranged on a single spherical surface concentric with the atom: the actual number which can be arranged in this way depends on the distribution of positive electricity in the inside of the atom. When the number of electrons exceeds this critical number, the electrons break up into two or more groups arranged in a series
