The determination of the rate of transmission of heat from the surface of a heated metal to water in contact with it, or from hot water to a colder surface, is a problem of some difficulty, but is of such great importance in the theory of boilers and surface condensers, that further investigation would seem to be justified, especially as, although the theory of the subject has been much studied, yet owing to practical difficulties, the constants involved, so far as the author is aware, have not been definitely determined for cases which occur in practice. Peclet’s experiments on the rate of transmission of heat from water to water across a metal plate, throw much light on the question. His experiments were made to determine the thermal conductivities of various metals by measuring the heat passed through a metal plate, one side of which was exposed to steam and the other to water which was kept agitated by a stirrer. In these experiments, Peclet found that the heat transmitted was sensibly independent of the nature and thickness of the metal used, the conclusion being that on each side of the plate there was a film of water through which the heat was transmitted by conduction, and that compared to these, the thermal resistance of the plate was small. This difficulty was overcome by an arrangement consisting of revolving brushes in contact with each side of the plate, so as to prevent the formation of a film on the surfaces, and by keeping the water in a violent state of agitation. In this way it was possible to keep the surfaces of the plate at the same temperature as the water in contact with them, and the conductivities of metals determined by this method agree with carefully determined conductivities obtained by other methods.