The α-binding energy as a function of the number of neutrons and protons is shown to exhibit sharp fluctuations which occur at more or less regular intervals. There is evidence that these kinks are caused by discontinuous changes in the density and radius of the nuclei. It is shown that a mathematical connection exists between kinks in the α-binding energy curve and the irregularities of the β-stability line (Gamow valley), so that both must occur in the same region of the nuclei. This applies also to the irregularities in the mass-defect curve. A study is made of the energies of β-decay (ΔM) of isobaric nuclei in the region of the radioactive elements. This shows that nuclei of odd mass-number A have a slightly higher binding energy for even proton number Z (a lower mass by 0.2 MeV.) than for odd Z. The effect, though well known for nuclei of even mass-numbers, has not before been observed for odd ones, where it is much smaller.