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(81.) As two motions simultaneously communicated to a body are equivalent to a single motion in an intermediate direction, so also a single motion may be mechanically replaced, by two motions in directions expressed by the sides of any parallelogram, whose diagonal represents the single motion. This process is “the resolution of motion,” and gives considerable clearness and facility to many mechanical investigations.

(82.) It is frequently necessary to express the portion of a given force, which acts in some given direction different from the immediate direction of the force itself. Thus, if a force act from A, fig.11., in the direction AC, we may require to estimate what part of that force acts in the direction AB. If the force be a pressure, take as many inches AP from A, on the line AC, as there are ounces in the force, and from P draw PM perpendicular to AB; then the part of the force which acts along AB will be as many ounces as there are inches in AM. The force AB is mechanically equivalent to two forces, expressed by the sides AM and AN of the parallelogram; but AN, being perpendicular to AB, can have no effect on a body at A, in the direction of AB, and therefore the effective part of the force AP in the direction AB is expressed by AM.