The foot-pound, which is the unit of mechanical force as established by Mr. Joule, is the force that would raise one pound of matter to the height of one foot; or it is the impetus or force generated by a body of one pound weight falling by its gravitation through the height of one foot. Now impetus or vis viva is equal to the mass of a body multiplied by the square of the velocity with which it is moving: it is the true measure of work or mechanical labour. For if a weight be raised ten feet, it will require four times the labour to raise an equal weight to forty feet. If both these weights be allowed to fall freely by their gravitation, at the end of their descent, their velocities will be as one to two, that is as the square roots of their heights, but the effect produced will be as their masses multiplied by one and four; but these are the squares of their velocities. Hence impetus or vis viva is equal to the mass multiplied by the square of the velocity. Thus impetus is the true measure of the labour employed to raise the weights, and of the effect of their descent, and is entirely independent of time. It is well known that iron becomes red-hot by percussion or impetus. The atoms of the iron are thrown into vibration, and these minute motions communicated to the nerves produce the sensation of heat. Now the mechanical labour required to raise the hammer to any number of feet is equal to the weight of the hammer multiplied by that number of feet; but the impetus or mechanical effect of the fall of the hammer is equal to its mass multiplied by the square of the velocity, that is to the vis viva: hence the quantity of heat generated is proportional to the vis viva. The circumstances being the same, if the mass be doubled the amount of heat is doubled; and if the velocity be doubled the amount of heat is quadrupled. If the weight and the perpendicular height through which a body has fallen be known, the quantity of heat generated may be determined. The same amount of heat is generated by the same amount of force, whatever that force may be, whether impetus, friction, or any other.