The problem of the diffusion and convection of heat from an arbitrarily placed heat source in the potential convection field due to uniform streaming past an infinite circular cylinder is considered. Solutions are obtained for the regions inside and outside the cylinder and are given in terms of Mathieu Functions. An appendix giving the required properties of these functions is included.

The problem of the diffusion and convection of heat from an arbitrarily placed source in the convection field due to a fluid producing dipole is considered. The solution for the temperature at any point in the fluid is found analytically. The isotherms and lines of constant flux are plotted.

The problem of the diffusion and convection of heat in two-dimensional, incompressible flow past a circular cylinder is considered. Solutions are found for the temperature at any point exterior to the cylinder in terms of the boundary conditions on the surface and two particular boundary conditions are considered.

Hazebroek's problem of a finite line-source in an infinite elastic medium is reconsidered. Here the object is to present a simpler method of solution by treating bhe line-source as equivalent to an appropriate distribution of point sources over the surface of a prolate spheroid which degenerates into this line in the limit when its minor axis tends to zero. This is achieved by using the property of Green's functions. The solution thus obtained is verified to be identical with that derived by Hazebroek.

Small variations in the elastic parameters of a solid medium give rise to scattering of elastic waves and hence to a reduction in their amplitudes. The attenuation coefficients associated with this process have been calculated for surface waves.

Expressions have been derived for waves with wavelengths long compared with the mean wavelength of the variation of the elastic parameters in space. The attenuation coefficients were found to be the same as if the attenuating mechanism were a particular type of visco-elasticity.

We consider some elastostatic and related potential problems in which an unbounded uniform medium contains a plane elliptic disc as an inhomogeneity. Various appropriate conditions on the disc and at infinity are specified. These problems have many physical applications. In the elastostatic case the disc can be a crack or rigid inclusion, for example. The potential problems include the classical one of finding the electrostatic field around an elliptic disc charged to a given potential.