We have seen how Rumford showed that heat was motion, and how he approximately determined its mechanical equivalent. Seguin, a nephew of Montgolfier, endeavoured to show that, when a steam-engine was working, less heat entered the condenser than when the same amount of steam was blown idly through the engine. This Hirn succeeded in showing, thus proving that heat was actually used up in doing work. Mayer, of Heilbronn, measured the work done in compressing air, and the heat generated by the compression, and assumed that the whole of the work done in the compression, and no more, was converted into the heat developed, which was the same thing as assuming that no work was done in altering the positions of the particles of gas. From these measurements he deduced a value of the mechanical equivalent of heat. The assumption which Mayer made was shown experimentally by Joule to be nearly correct. Joule proved that, when air expands from a high pressure into a vacuum, no heat is generated or absorbed on the whole. This he did by compressing air in an iron bottle, which was connected with another bottle from which the air had been exhausted, the connecting tube being closed by a stop-cock. The whole apparatus was immersed in a bath of water, and on allowing the air to rush from one vessel into the other, and then stirring the water, the temperature was found to be the same as before. When the iron bottles were in separate baths of water, that from which the air rushed was cooled, and that into which it rushed was heated to the same extent. Joule and Thomson afterwards showed that a very small amount of heat is absorbed in this experiment. Joule also showed that the heat generated in a battery circuit is proportional to the product of the electro-motive force and the current, or to the product of the resistance and the square of the current, which, in virtue of Ohm's law, is the same thing. This relation is often known as Joule's law. He also proved that, for the same amount of chemical action in the battery, the heat generated was the same, whether it were all generated within the battery or part in the battery and part in an external wire; and that in the latter case, if the wire became so hot as to emit light, the heat measured was less than before, on account of the energy radiated as light. With a magneto-electric machine he employed mechanical power to produce a current, and the energy of the current he converted into heat. In all cases he found that, _whatever transformations the energy might undergo in its course, a definite amount of mechanical energy, if entirely converted into heat, always produced the same amount of heat_; and he thereby proved, not only that heat is essentially _motion_, but that it corresponds precisely with that particular dynamical quantity which is called _energy_; and thus justified the attempt to find a relation between heat and energy, or to express the mechanical equivalent of heat as so many foot-pounds.