(132.) Hence it may easily be inferred, that the force down the plane is uniform; for since the weight of the body P is always the same, and since its proportion to that part which urges it down the plane is the same, it follows that the quantity of this part cannot vary. The motion of a heavy body down an inclined plane is therefore an uniformly-accelerated motion, and is characterised by all the properties of uniformly-accelerated motion, explained in the last chapter. Since P F represents the force of gravity, that is, the force with which the body would descend freely in the vertical direction, and P C the force with which it moves down the plane, it follows that a body would fall freely in the vertical direction from P to F in the same time as on the plane it would move from P to C. In this manner, therefore, when the height through which a body would fall vertically is known, the space through which it would descend in the same time down any given inclined plane may be immediately determined. For let A B, _fig. 25._, be the given inclined plane, and let P F be the space through which the body would fall in one second. From F draw F C perpendicular to the plane, and the space P C is that through which the body P will fall in one second on the plane. (133.) As the angle B A H, which measures the elevation of the plane, is increased, the obliquity of the vertical direction P F with the plane is also increased. Consequently, according to what has been proved (130), it follows, that as the elevation of the plane is increased, the force which urges the body down the plane is also increased, and as the elevation is diminished, the force suffers a corresponding diminution. The two extreme cases are, 1. When the plane is raised until it becomes perpendicular, in which case the weight is permitted to fall freely, without exerting any pressure upon the plane; and, 2. When the plane is depressed until it becomes horizontal, in which case the whole weight is supported, and there is no motion. From these circumstances it follows, that by means of an inclined plane we can obtain an uniformly-accelerating force of any magnitude less than that of gravity. We have here omitted, and shall for the present in every instance omit, the effects of _friction_, by which the motion down the plane is retarded. Having first investigated the mechanical properties of bodies supposed to be free from friction, we shall consider friction separately, and show how the present results are modified by it. (134.) The accelerating forces on different inclined planes may be compared by the principle explained in (131). Let _figs. 25._ and _26._ be two inclined planes, and take the lines P F in each figure equal, both expressing the force of gravity, then P C will be the force which in each case urges the body down the plane.