A medium with periodic variation of the dielectric tensor is considered. It is assumed to have helical symmetry. The response to external fields is described by the most general linear law—that is, by the methods of spatial dispersion theory. The propagation of a wave is described by a mutually consistent electric field and polarisation. It is shown that the presence of the medium produces changes in the polarisation and wave vector of the electric field, and the selection rules governing these changes are derived from symmetry. The results generalise previous work on the Oseen model for a cholesteric liquid crystal to the case when the molecules are not perpendicular to the helical axis. This can arise in an external magnetic field applied along this axis.

The possibility of extending the well known Poincare sphere representation of polarised light to include phase is considered. Any attempt to define the zero of phase for each vibration represented on the Poincare sphere runs into discontinuities at at least one point. These are shown to be inevitable using a topological argument.

The thermal properties of ionic crystals are analysed using the variational principle of classical statistical mechanics. The Einstein and Debye pictures of the lattice vibrations are adopted as trial Hamiltonians. No explicit calculation of the lattice spectrum is needed. The variational result for the thermal expansion in the Einstein picture is identical to that recently derived by Narayan and Ramaseshan by a physically motivated thermal force picture. The agreement with experimental values in the alkali halide family of crystals is surprisingly good, the root mean square error being about 14%. The parameters in the interionic potential used are obtained from the lattice spacings and compressibilities of the crystals and not from anharmonic properties. The Debye picture gives about equally good results for the thermal expansion, but better results for the thermal vibration amplitudes of the ions. It differs from the Einstein picture in incorporating correlated vibrations of atoms and in having an explicit Coulomb contribution to the thermal properties. It is suggested that the theory given in this paper has a useful role to play in studies of thermal expansion and phase stability for large families of ionic crystals when combined with semi-empirical theories.

The broad area of galactic dynamics is presented for a physics audience, with the requisite astronomy background in outline, and focusing on gravitational effects. The basic underlying model is a large number of particles (which could be stars or dark matter) moving in their self-consistent gravitational potential. The effects of two-particle correlations/scattering, although weak, can be cumulative and hence important for a class of systems such as star clusters which are hence termed collisional. On the larger scale of galaxies, we have collisionless behaviour which is different and in some ways richer. The basic ideas and applications in both these regimes are described, and some issues highlighted in conclusion.