In the elements of physics it is nowadays taught that mechanical work may be transformed into heat, and reciprocally that heat may be transformed into mechanical work. Friction, impact, pressure, and expansion destroy or annihilate the mechanical energy communicated to a body or to the organs of a machine. With the disappearance of motion we note the appearance of heat. Examples abound. The tyre of a wheel is heated by the friction of the road. Portions of steel are warmed by the impact with stone, as in the old flint and steel. Two pieces of ice were melted by Davy, who rubbed them one against the other, the external temperature being below zero. The boiling of a mass of water caused by a drill was noticed by Rumford in 1790, during the manufacture of bronze cannon. Metal, beaten on an anvil, is heated. A leaden ball flattened against a resisting obstacle shows increase of temperature carried to the point of fusion. Finally, and symbolically, we have the origin of fire in the fable of Prometheus, by rubbing together the pieces of wood which the Hindoos called _pramantha_. Correlation is constant between the thermal and mechanical phenomena, a correlation that becomes evident as soon as observers have ceased to restrict themselves to the determination in isolation of the one fact or the other. There is never any real destruction of heat and motion in the true sense of the word; what disappears in one form appears again in another; just as if something indestructible were appearing in a series of successive disguises. This impression is translated into words when we speak of the metamorphosis of mechanical into thermal energy. _The Mechanical Equivalent of Heat._—The interpretation assumes a remarkable character of precision, which at once strikes the mind when physics applies to these transformations the almost absolute accuracy of its measurements. We then find that the rate of exchange is invariable. Transformations of heat into motion, and of motion into heat, take place according to a rigorous numerical law, which brings into exact correspondence the quantity of each. Mechanical effect is estimated, as we have seen, by work, that is in kilogrammetres. Heat is measured in calories, the calorie being the quantity of heat necessary to raise from 0°C to 1°C a kilogramme of water (Calorie) or one gramme of water (calorie). It is found that whatever may be the bodies and the phenomena which serve as intermediaries for carrying out this transformation, we must always expend 425 kilogrammetres to create a Calorie, or expend 0·00234 Calories to create a kilogrammetre. The number 425 is the mechanical equivalent of the Calorie, or, as is incorrectly stated, of the heat. It is this constant fact which constitutes _the principle of the equivalence of heat and of mechanical work_. § 5. CHEMICAL ENERGY.