Rumford had noted the very great evolution of heat when gun-metal was rubbed by a blunt borer, and had come to the reasonable conclusion that what was evolved in apparently unlimited quantity by the abrasion or cutting down of a negligible quantity of materials could not be a material substance. He had also made a rough estimate of the relation between the work spent in driving the borer by horse-power and the heat generated. Joule's method of determining the work-equivalent of heat was a refinement of Rumford's, but differed in the all-important respect that accurate means were employed for measuring the expenditure of work and the gain of heat. He stirred a liquid, such as water or mercury, in a kind of churn driven by a falling weight. The range of descent of the weight enabled the work consumed to be exactly estimated, and a sensitive thermometer in the liquid measured the rise of temperature; thus the heat produced was accurately determined. The rise of temperature was very slight, and the change of state of the liquid, and therefore any possible change in its internal energy, was infinitesimal. The experiments were carried out with great care, and included very exact measurements of the various corrections--for example, the amount of work spent at pulleys and pivots without affecting the liquid, and the loss of heat by radiation. The experiments proved that the work spent on the liquid and the heat produced were in direct proportion to one another. He found, finally, in 1850, that 772 foot-pounds of work at Manchester generated one British thermal unit, that is, as much heat as sufficed to raise a pound of water from 60° F. to 61° F. An approximation to this conclusion was contained in the paper which he communicated to the British Association at Oxford in 1847. The results of a later determination made with an improved apparatus, and completed in 1878, gave a very slightly higher result. When corrected to the corresponding Fahrenheit degree on the air thermometer it must be increased by somewhat less than one per cent. The exact relation has been the subject during the last twenty years of much refined experimental work, but without any serious alteration of the number indicated above. It is probable that in consequence of the conference which he had with Joule at Oxford Thomson had his thoughts turned for some time almost exclusively to the dynamical theory of heat engines. He worked at the subject almost continuously for a long time, sending paper after paper to the Edinburgh Royal Society. As we have seen, he had given Joule a description of Carnot's essay on the Motive Power of Heat and the conclusions, or some of them, therein contained. Joule's result, and the thermodynamic law which it established, gave the key to the correction of Carnot's theory necessary to bring it into line with a complete doctrine of energy, which should take account of work done against frictional resistances.