nd 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.

[Illustration: 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).

[Illustration: 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?

159. The Screw. Another valuable and indispensable form of the
inclined plane is the screw. This consists of a metal rod around which
passes a ridge, and Figure 108 shows clearly that a screw is simply a
rod around which (in effect) an inclined plane has been wrapped.

[Illustration: FIG. 108--A screw as a simple machine.]

The ridge encircling the screw is called the thread, and the distance
between two successive threads is called the pitch. It is easy to see
that the closer the threads and the smaller the pitch, the greater the
advantage of the screw, and hence the less force needed in overcoming
resistance. A corkscrew is a familiar illustration of the screw.

160. Pulleys. The pulley, another of the machines, is merely a
grooved wheel around which a cord passes. It is sometimes more
convenient to move a load in one direction rather than in another, and
the pulley in its simplest form enables us to do this. In order to
raise a flag to the top of a mast, it is not necessary to climb the
mast,