16. Another mode of inquiring into the natural measure of heat is to seek it by researches on the _law of cooling_ of hot bodies. If we assume that the process of cooling of hot bodies consists in a certain material heat flying off, we may, by means of certain probable hypotheses, determine mathematically the law according to which the temperature decreases as time goes on; and we may assume _that_ to be the true measure of temperature which gives to the experimental law of cooling the most simple and probable form. It appears evident from the most obvious conceptions which we can form of the manner in which a body parts with its superabundant heat, that the hotter a body is, the faster it cools; though it is not clear without experiment, by what law the rate of cooling will depend upon the heat of the body. Newton took for granted the most simple and seemingly natural law of this dependence: he supposed the rate of cooling to be _proportional_ to the temperature, and from this supposition he could deduce the temperature of a hot iron, calculating from the original temperature and the time during which it had been cooling. By calculation founded on such a basis, he graduated his thermometer. 17. But a little further consideration showed that the rate of cooling of a hot body depended upon the temperature of the surrounding bodies, as well as upon its own temperature. Prevost's _Theory of Exchanges_[33\4] was propounded with a view of explaining this dependence, and was generally accepted. According to this theory, all bodies radiate heat to one another, and are thus constantly giving and receiving heat; and a body which is hotter than surrounding bodies, cools itself, and warms the surrounding, bodies, by an exchange of heat for heat, in which they are the gainers. Hence if _θ_ be the temperature of the bodies, or of the space, by which the hot body is surrounded, and _θ_ + _t_ the temperature of the hot body, the rate of cooling will depend {352} upon the excess of the radiation for a temperature _θ_ + _t_, above the radiation for a temperature _θ_. [Note 33\4: _Recherches sur la Chaleur_, 1791. _Hist. Ind. Sc._ b. x. c. i. sect. 2.]