In this paper the Mechanical Theory of Thermo-electric Currents in linear conductors of non-crystalline substance, first communicated to the Royal Society December 15, 1851, is extended to solids of any form and of crystalilne substance.

It is first proved, that if a solid be such that bars cut from it in different directions have different thermo-electric powers relatively to one another, or to other linear conductors, forming part of a circuit, there must, for every bar cut from it, except in certain particular directions (principal thermo-electric axes), be a new thermo-electric quality, of a kind quite distinct from any hitherto known; giving rise to a reciprocal thermo-dynamic action, which consists of a difference in temperature at the sides of the bar causing a current to flow longitudinally, when the two ends, being at the same temperature, are connected by a uniformly heated conductor; and a current through the bar causing an absorption and evolution of heat at its two sides, when these are kept at the same temperature.