Another subject that engaged his attention at this time, was an examination of the scale of the thermometer, to learn whether equal differences of expansion corresponded to equal additions or abstractions of heat. His mode was to mix together equal weights of water of different temperatures, and to measure the temperature of the mixture by a thermometer. It is obvious that the temperature must be the exact mean of that of the two portions of water; and that if the expansion or contraction of the mercury in the thermometer be an exact measure of the difference of temperature, a thermometer, so placed, will indicate the exact mean. Suppose one pound of water at 100° to be mixed with one pound of water at 200°, and the whole heat still to remain in the mixture, it is obvious that it would divide itself equally between the two portions of water. The water of 100° would become hotter, and the water of 200° would become colder: and the increase of temperature in the colder portion would be just as much as the diminution of temperature in the hotter portion. The colder portion would become hotter by 50°, while the hotter portion would become colder by 50°. Hence the real temperature, after mixture, would be 150°; and a thermometer plunged into such a mixture, if a true measurer of heat, would indicate 150°. The result of his experiments was, that as high up as he could try by mixing water of different temperatures, the mercurial thermometer is an accurate measurer of the alterations of temperature. An account of his experiments on this subject was drawn up by him, and read to the literary society of the College of Glasgow, on the 28th of March, 1760. Dr. Black, at the time he made these experiments, did not know that he had been already anticipated in them by Dr. Brooke Taylor, the celebrated mathematician, who had obtained similar results, and had consigned his experiments to the Royal Society, in whose Transactions for 1723 they were published. It has been since found by Coulomb and Petit, that at higher temperatures than 212° the rate of the expansion of mercury begins to increase. Hence it happens that at high temperatures the expansion of mercury is no longer an accurate measurer of temperature. Fortunately, the expansion of glass very nearly equals the increment of that of mercury. The consequence is, that in a common glass-thermometer mercury measures the true increments of temperature very nearly up to its boiling point; for the boiling point of mercury measured by an air-thermometer is 662°: and if a glass mercurial thermometer be plunged into boiling mercury, it will indicate 660°, a difference of only 2° from the true point.