The slope of the road is called its grade, and the grade itself is simply the number of feet the hill rises per mile. A road a mile long (5280 feet) has a grade of 132 if the crest of the hill is 132 feet above the level at which the road started.
FIG. 106.—A long, gradual ascent is better than a shorter, steeper one.
In such an incline, the ratio of length to height is 5280 ÷ 132, or 40; and hence in order to pull a train of cars to the summit, the engine would need to exert a continuous pull equal to one fortieth of the combined weight of the train.
If, on the other hand, the ascent had been gradual, so that the grade was 66 feet per mile, a pull from the engine of one eightieth of the combined weight would have sufficed to land the train of cars at the crest of the grade.
Because of these facts, engineers spend great sums in grading down railroad beds, making them as nearly level as possible. In mountainous regions, the topography of the land prevents the elimination of all steep grades, but nevertheless the attempt is always made to follow the easiest grades.
158. The Wedge. If an inclined plane is pushed underneath or within an object, it serves as a wedge. Usually a wedge consists of two inclined planes (Fig. 107).
FIG. 107.—By means of a wedge, the stump is split.
A chisel and an ax are illustrations of wedges. Perhaps the most universal form of a wedge is our common pin. Can you explain how this is a wedge?