An investigation of the nature of vibrational modes in a structurally disordered solid and the thermal conduction properties of such a solid is described. Analogies between the vibrational mode problem and the subject of electrons moving in a disordered system of potential wells are discussed and a method for calculating the electronic band structure of perfect solids proposed by Ziman (1965) is interpreted, compared with the A.P.W. method and used to consider the scattering of a Bloch wave from an impurity potential.