We can know only from _experience_ that mechanical processes produce other physical transformations, or _vice versa_. The attention was first directed to the connexion of mechanical processes, especially the performance of work, with changes of thermal conditions by the invention of the steam-engine, and by its great technical importance. Technical interests and the need of scientific lucidity meeting in the mind of S. Carnot led to the remarkable development from which thermodynamics flowed. It is simply _an accident of history_ that the development in question was not connected with the practical applications of _electricity_. In the determination of the maximum quantity of _work_ that, generally, a heat-machine, or, to take a special case, a steam-engine, can perform with the expenditure of a _given_ amount of heat of combustion, Carnot is guided by mechanical analogies. A body can do work on being heated, by expanding under pressure. But to do this the body must receive heat from a _hotter_ body. Heat, therefore, to do work, must pass from a hotter body to a colder body, just as water must fall from a higher level to a lower level to put a mill-wheel in motion. Differences of temperature, accordingly, represent forces able to do work exactly as do differences of height in heavy bodies. Carnot pictures to himself an ideal process in which no heat flows away unused, that is, without doing work. With a given expenditure of heat, accordingly, this process furnishes the maximum of work. An analogue of the process would be a mill-wheel which scooping its water out of a higher level would slowly carry it to a lower level without the loss of a drop. A peculiar property of the process is, that with the expenditure of the same work the water can be raised again exactly to its original level. This property of _reversibility_ is also shared by the process of Carnot. His process also can be reversed by the expenditure of the same amount of work, and the heat again brought back to its original temperature level. Suppose, now, we had _two_ different reversible processes _A_, _B_, such that in _A_ a quantity of heat, _Q_, flowing off from the temperature _t₁_ to the lower temperature _t₂_ should perform the work _W_, but in _B_ under the same circumstances it should perform a greater quantity of work _W_ + _W'_; then, we could join _B_ in the sense assigned and _A_ in the reverse sense into a _single_ process. Here _A_ would reverse the transformation of heat produced by _B_ and would leave a surplus of work _W'_, produced, so to speak, from nothing. The combination would present a perpetual motion.