By means of a variation principle applied to a nuclear wave function for four nucleons in the field of a closed core, equations are derived giving the relative proportions of a component describing an alpha-particle group and components describing the four nucleons in shell-model states with spin-orbit coupling wave functions, the two neutron states and the two proton states each paired to give zero resultant angular momentum. Numerical calculations, taking into account only 1h2/3 states for protons and the 2g3/2 states for neutrons, give the alpha-group wave function a relative weight (in the linear combination) of about 1%.

Second-order perturbation theory, in conjunction with the usual treatment of electron-phonon interaction, allows us to calculate the correction to the first-order result for the scattering of phonons by electrons. It is shown that the second-order term is much smaller, and therefore negligible. This justifies the use of the first-order theory in the treatment of the interaction in metals and semi-conductors.

An investigation is made of the deformation and flow properties of two-dimensional disperse systems consisting of small circular patches of one component widely dispersed in a continuous component with different rheological properties. Attention is restricted to small deformations (or small rates of deformation in the case of a fluid system) so that the equations of state are linear and the properties of each component can be characterized by two elastic moduli, or by two operators involving d/dt which take the place of moduli. Surface tension in each component and boundary tension between the components are taken into account, so that the theory can be applied to interfacial films at liquid-liquid or liquid-gas interfaces as well as to thicker sheets and films. General formulae are derived, expressing the two modulus operators of a disperse system in terms of those of the components, and their use is illustrated by means of examples.

The deflexion at any point of a thin circular plate subjected to certain loadings along the circumference or over the area of an eccentric circle is obtained when the plate is supported at several points along the boundary, the supports being symmetrically situated with respect to the common diameter of the plate and circle.