_MECHANICS._—The whole momentum or quantity of force of a moving body, is the result of the quantity of matter, multiplied by the velocity with which it is moved; and when the product arising from the multiplication of the particular quantities of matter in any two bodies, by their respective velocities are equal, their momentum will be so too. Upon this easy principle depends the whole of mechanics; and it holds universally true, that when two bodies are suspended on any machine, so as to act contrary to each other; if the machine be put in motion, and the perpendicular ascent of one body multiplied into its weight, be equal to the perpendicular descent of the other, multiplied into its weight: those bodies, how unequal soever in their weights, will balance each other in all situations: for, as the whole ascent of the one is performed in the same time as the whole descent of the other, their respective velocities must be as the spaces they move through; and the excess of weight in one is compensated by the excess of velocity in the other. Upon this principle it is easy to compute the power of any engine, either simple or compound; for it is only finding how much swifter the power moves than the weight does, (_i. e._ how much further in the same time,) and just so much is the power increased by the help of the engine. The simple machines usually called mechanic powers, are six in number, _viz._ the _Lever_, the _Wheel and Axle_, the _Pulley_, the _Inclined Plane_, the _Wedge_, and the _Screw_. There are four kinds of _Levers_: 1st, Where the prop is placed between the weight and the power. 2d, Where the prop is at one end of the lever, the power at the other, and the weight between them. 3d, Where the prop is at one end, the weight at the other, and the power applied between them. 4th, The bended lever, which differs from the first in form, but not in property. In the first and 2d kind, the advantage gained by the lever, is as the distance of the power from the prop, to the distance of the weight from the prop. In the 3d kind, that there may be a balance between the power and the weight, the intensity of the power must exceed the intensity of the weight, just as much as the distance of the weight from the prop exceeds the distance of the power from the prop. As this kind of lever is disadvantageous to the moving power, it is seldom used. _Wheel and Axle._—Here the velocity of the power is to the velocity of the weight, as the circumference of the wheel is to the circumference of the axle. _Pulley._—A single pulley, that only turns on its axis, and does not move out of its place, serves only to change the direction of the power, but gives no mechanical advantage. The advantage gained in this machine, is always as twice the number of _moveable_ pullies; without taking any notice of the _fixed_ pullies necessary to compose the system of pullies.