(127.) The laws which govern the descent of bodies by gravity, being reversed, will be applicable to the ascent of bodies projected upwards. If a body be projected directly upwards with any given velocity, it will rise to the height from which it should have fallen to acquire that velocity. The earth’s attraction will, in this case, gradually deprive the body of the velocity which is communicated to it at the moment at which it is projected. Consequently, the phenomenon will be that of _retarded motion_. At each part of its ascent it will have the same velocity which it would have if it descended to the same place from the highest point to which it rises. Hence it is clear, that all the particulars relative to the ascent of bodies may be immediately inferred from those of their descent, and therefore this subject demands no further notice. To complete the investigation of the phenomena of falling bodies, it would now only remain to explain the method of ascertaining the exact height through which a body would descend in one second, if unresisted by the atmosphere, or any other disturbing cause. As the solution of this problem, however, requires the aid of principles not yet explained, it must for the present be postponed. CHAP. VIII. OF THE MOTION OF BODIES ON INCLINED PLANES AND CURVES. (128.) In the last chapter, we investigated the phenomena of bodies descending freely in the vertical direction, and determined the laws which govern, not their motion alone, but that of bodies urged by any uniformly accelerating force whatever. We shall now consider some of the most ordinary cases in which the free descent of bodies is impeded, and the effects of their gravitation modified. (129.) If a body, urged by any forces whatever, be placed upon a hard unyielding surface, it will evidently remain at rest, if the resultant (76) of all the forces which are applied to it be directed perpendicularly against the surface. In this case, the effect produced is pressure, but no motion ensues. If only one force act upon the body, it will remain at rest, provided the direction of that force be perpendicular to the surface. But the effect will be different, if the resultant of the forces which are applied to the body be oblique to the surface. In that case this resultant, which, for simplicity, may be taken as a single force, may be considered as mechanically equivalent to two forces (76), one in the direction of the surface, and the other perpendicular to it. The latter element will be resisted, and will produce a pressure; the former will cause the body to move. This will perhaps be more clearly apprehended by the aid of a diagram. Let A B, _fig. 25._, be the surface, and let P be a particle of matter placed upon it, and urged by a force in the direction P D, perpendicular to A B. It is manifest, that this force can only press the particle P against A B, but cannot give it any motion.