Earlier studies by Thompson and Feather have been extended to lighter nuclei, wherever the half-life, branching ratios, and transition energy $W$ are known, and a Sargent diagram constructed for 87 electron capture transitions; $W$, defined as the energy of the neutrino emitted during capture, must be deduced indirectly, from atomic mass differences, positron spectra, or inner bremsstrahlung. Known allowed transitions fall considerably below the line proposed by Feather, but the scatter of the points does not permit differentiation of Sargent curves for different degrees of forbiddenness. Comparative half-lives have been calculated for these capture transitions, and are tabulated and compared with $\mathrm{ft}$ values for beta emitters. The distribution of $\mathrm{ft}$ values are similar, and agreement is evident between most $\mathrm{ft}$ values for electron capture and positron emission in the same transformation.

A method of obtaining the angular parts of one electron wave functions in all crystal lattices is discussed. The functions are shown to be bases for irreducible representations of rotation groups. Tables of these functions are given for use in cubic and close packed hexagonal lattices. Consideration is also given to angular wave functions in polyatomic crystals.

A study is made of the convergence of the Born expansions in collision problems involving a static central potential. The scattering of each partial wave, characterized by the phase shift ${\eta }_l$, is treated separately. Estimates of the radii of convergence of $tan{\eta }_l$ and of $S_l\equiv e^{2i{\eta }_l}$ (as well as of the corresponding wave functions) are established, and the truncation errors due to breaking off the Born expansions are investigated. An appendix deals with the expansion of ${\eta }_l$ itself.

The use of a rotating coordinate system to solve magnetic resonance problems is described. On a coordinate system rotating with the applied rotating magnetic field the effective field is reduced by the Larmor field appropriate to the rotational frequency. However, on such a coordinate system problems can more readily be solved since there is no time variation of the field. The solution in a stationary frame of reference is then obtained by a transformation from the rotating to the stationary frame. This procedure is equally valid in classical and in quantum-mechanical problems. The method is applied both to the molecular beam magnetic resonance method and to resonance absorption and nuclear induction experiments.

The paper gives recalculated values of the energies of natural alpha particles which have been measured precisely by deflection methods. The results are based on the new values for the Faraday and the mass of the ${\mathrm{He}}^4$ atom, a revised value for the author's absolute determination of the main group of RaC' and weighted mean values for the main groups of Th${\mathrm{C}}^{212}$, Th${\mathrm{C}\text{'}}^{212}$, and ${\mathrm{Po}}^{210}$.