One of the mechanic powers or simple machines by which weights may be elevated with great facility. If a heavy body be suspended freely in space, or against a vertical plane, it is manifest that a weight equal to itself must be employed to sustain it. If, on the other hand, it rest on a horizontal plane, the whole weight is sustained by the plane. But if the body rest on a plane at all inclined to the horizon, a part only of the weight is sustained by the plane. Let A B be a plane inclined to the horizon; D, a body supported on the plane by means of the weight or power E; if the experiment be made by carrying a cord over a fixed pulley, as in the diagram, it will be seen that while the cord continues parallel to the plane, the power E will bear to the weight D the same proportion as B C to B A; that is, as the height of the plane to its length. If the length of A B be six feet, and the height one foot, a power of one pound will balance six pounds on the plane; if the height be two feet, one pound will balance three, and so on. To ascertain the power obtained by this contrivance we must therefore divide the length of the plane by the height.
If the power act parallel to the base, the power is to the weight as the height is to the length of the base.
When the power acts parallel to the plane, the power, weight, and pressure on the plane will be proportional to the three lines B C, B A, and A C. For if the weight be represented by a b, by the resolution of forces this may be decomposed into ac, c b, one perpendicular and the other parallel to the plane. Now it is clear that the one which acts perpendicularly on the plane will exert an equivalent pressure, while the part that is parallel to the plane must be sustained by the power. Hence the power, weight, and pressure, are proportional to the sides of the small triangle a b c, which is similar to the large one A B C. If. the end of the cord be raised above the parallel direction, the pressure on the plane will be diminished, but if it be depressed below the parallel direction, the pressure will be increased, but in both cases a greater power will be required to move the body up the plane. It is, we apprehend, needless to state examples of the application of this method of increasing our power, as its use in assisting to raise bodies to small elevations must be abundantly obvious.