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(74.) If two forces act upon the same point of a body in different directions, a single force may be assigned, which, acting on that point, will produce the same result as the united effects of the other two.

Let P, fig.7., be the point on which the two forces act, and let their directions be PA and PB. From the point P, upon the line PA, take a length P a, consisting of as many inches as there are ounces in the force PA; and, in like manner, take P b, in the direction PB, consisting of as many inches as there are ounces in the force PB. Through a draw a line parallel to PB, and through b draw a line parallel to PA, and suppose that these lines meet at c. Then draw PC. A single force, acting in the direction PC, and consisting of as many ounces as the line Pc consists of inches, will produce upon the point P the same effect as the two forces PA and PB produce acting together.

(75.) The figure P acb is called in GEOMETRY a parallelogram; the lines P a, P b, are called its sides, and the line P c is called its diagonal. Thus the method of finding an equivalent for two forces, which we have just explained, is generally called “the parallelogram of forces,” and is usually expressed thus: “If two forces be represented in quantity and direction by the sides of a parallelogram, an equivalent force will be represented in quantity and direction by its diagonal.”