(79.) In the examples of the composition of forces which we have here given, the effects of the forces are the production of pressures, or, to speak more correctly, the theorem which we have illustrated, is “the composition of pressures.” For the point P is supposed to be at rest, and to be drawn or pressed in the directions P M and P N. In the definition which has been given of the word force, it is declared to include motions as well as pressures. In fact, if motion be resisted, the effect is converted into pressure. The same cause acting upon a body, will either produce motion or pressure, according as the body is free or restrained. If the body be free, motion ensues; if restrained, pressure, or both these effects together. It is therefore consistent with analogy to expect that the same theorems which regulate pressures, will also be applicable to motions; and we find accordingly a most exact correspondence. (80.) If a body have a motion in the direction A B, and at the point P it receive another motion, such as would carry it in the direction P C, _fig. 10._, were it previously quiescent at P, it is required to determine the direction which the body will take, and the speed with which it will move, under these circumstances. Let the velocity with which the body is moving from A to B be such, that it would move through a certain space, suppose P N, in one second of time, and let the velocity of the motion impressed upon it at P be such, that if it had no previous motion it would move from P to M in one second. From the point M draw a line parallel to P B, and from N draw a line parallel to P C, and suppose these lines to meet at some point, as O. Then draw the line P O. In consequence of the two motions, which are at the same time impressed upon the body at P, it will move in the straight line from P to O. Thus the two motions, which are expressed in quantity and direction by the sides of a parallelogram, will, when given to the same body, produce a single motion, expressed in quantity and direction by its diagonal; a theorem which is to motions exactly what the former was to pressures. There are various methods of illustrating experimentally the composition of motion. An ivory ball, being placed upon a perfectly level square table, at one of the corners, and receiving two equal impulses, in the directions of the sides of the table, will move along the diagonal. Apparatus for this experiment differ from each other only in the way of communicating the impulses to the ball. (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.