Mechanical powers. When two heavy bodies or weights are made by any contrivance to act against each other, so as mutually to prevent each other, from being put into motion by gravity, they are said to be in equilibrio. The same expression is used with respect to other forces, which mutually prevent each other from producing motion.
Any force may be compared with gravity, considered as a standard. Weight is the action of gravity on a given mass. Whatever therefore is proved concerning the weights of bodies will be true in like circumstances of other forces.
Weights are supposed to act in lines of direction parallel to each other. In fact, these lines are directed to the centre of the earth, but the angle formed between any two of them within the space occupied by a mechanical engine is so small, that the largest and most accurate astronomical instruments are scarcely capable of exhibiting it.
The simplest of those instruments, by means of which weights or forces are made to act in opposition to each other, are usually termed mechanical powers. Their names are, the lever, the axis or axle, and wheel, the pully or tackle, the inclined plane, the wedge, and the screw.
Of the Lever.
The lever is defined to be a moveable and inflexible line, acted upon by three forces, the middle one of which is contrary in direction to the other two.
One of these forces is usually produced by the re-action of a fixed body, called the fulcrum.
If two contrary forces be applied to a lever at unequal distances from the fulcrum, they will equiponderate when the forces are to each other in the reciprocal proportion of their distances. For, by the resolution of force it appears, that if two contrary forces be applied to a straight lever, at distances from the fulcrum in the reciprocal proportion of their quantities, and in directions always parallel to each other, the lever will remain at rest in any position.
Since of the three forces which act on the lever, the two which are applied at the extremes, are always in a contrary direction to that which is applied in the space between them: this last force will sustain the effects of the other two; or, in other words, if the fulcrum be placed between the weights, it will be acted upon by their difference.
On the principle of the lever are made, scales for weighing different quantities of various kinds of things; the steelyard, which answers the same purpose by a single weight, removed to different distances from the fulcrum on a graduated arm, according as the body to be weighed is more or less in quantity; and the bent lever balance, which, by the revolution of a fixed weight, increasing in power as it ascends in the arc of a circle, indicates the weight of the counterpoise.