New relations which concern the existence and stability of atomic nuclei are presented, together with a discussion of evidence for the relations given earlier as exhibited by the newer data on the existence of isotopes. It is shown that the four series, the helium, uranium, lithium and beryllium series, exhibit a considerable amount of regularity and are now almost continuous. The more abundant species of odd atomic number keep in general to a constant isotopic number as the atomic number increases, or else the isotopic number increases by the same amount as the atomic number. There is a general tendency as the atomic number increases for the isotopic number of the most abundant isotope of elements of both even and odd atomic number (a) to remain constant, (b) to increase at the same rate as the atomic number or (c) to decrease along a line of constant electronic number.

The atomic, mass, isotopic, and electronic numbers of all known isotopes are given in figures which exhibit the periodic and other relations of atomic nuclei. Many undiscovered atomic species (isotopes of each element) between atomic numbers 61 and 18, are predicted, and the general relations predict the existence of a considerable number of additional species among elements of lower number.

These relations are presented in the form of fourteen rules, several of which are new, and three are fundamental laws presented earlier. The bearing of the newer data on these rules is discussed.

The paper discusses nuclear stability and abundance as related to the pairing of nuclear electrons and the oddness and evenness of the electronic number, to the evenness and oddness of the nuclear charge (atomic number) as exhibited by the most recent work on the composition of the crust of the earth, the meteorites, and the atmosphere of the sun, and to the ratio of nuclear electrons to protons.

The neutron, or nuclear neutral particle may play a part in atom building. The figures, fundamental laws, rules, and relations presented, especially the principle of continuity and regularity of series, when taken in connection with known facts, seem to indicate that atomic nuclei are built in steps, and, except in the simplest cases, not as single events. That is the general picture revealed by all of these appears to be in discord with the theory of Millikan and Cameron.

• Received 6 August 1931

DOI:https://doi.org/10.1103/PhysRev.38.1270