and so pull up the flag; the same result is accomplished much
more easily by attaching the flag to a movable string, somewhat as in
Figure 109, and pulling from below. As the string is pulled down, the
flag rises and ultimately reaches the desired position.

If we employ a stationary pulley, as in Figure 109, we do not change
the force, because the force required to balance the load is as large
as the load itself. The only advantage is that a force in one
direction may be used to produce motion in another direction. Such a
pulley is known as a fixed pulley.

[Illustration: FIG. 109.--By means of a pulley, a force in one
direction produces motion in the opposite direction.]

161. Movable Pulleys. By the use of a movable pulley, we are able to
support a weight by a force equal to only one half the load. In Figure
109, the downward pull of the weight and the downward pull of the hand
are equal; in Figure 110, the spring balance supports only one half
the entire load, the remaining half being borne by the hook to which
the string is attached. The weight is divided equally between the two
parts of the string which passes around the pulley, so that each
strand bears only one half of the burden.

We have seen in our study of the lever and the inclined plane that an
increase in force is always accompanied by a decrease in distance, and
in the case of the pulley we naturally look for a similar result. If
you raise the balance (Fig. 110) 12 feet, you will find that the
weight rises only 6 feet; if you raise the balance 24 inches, you will
find that the weight rises 12 inches. You must exercise a force of
100 pounds over 12 feet of space in order to raise a weight of 200
pounds a distance of 6 feet. When we raise 100 pounds through 12 feet
or 200 pounds through 6 feet the total work done is the same; but the
pulley enables those who cannot furnish a force of 200 pounds for the
space of 6 feet to accomplish the task by furnishing 100 pounds for
the space of 12 feet.

[Illustration: FIG. 110.--A movable pulley lightens labor.]

162. Combination of Pulleys. A combination of pulleys called block
and tackle is used where very heavy loads are to be moved. In Figure
111 the upper block of pulleys is fixed, the lower block is movable,
and one continuous rope passes around the various pulleys. The load is
supported by 6 strands, and each strand bears one sixth of the load.
If the hand pulls with a force of 1 pound at _P_, it can rais