e a load
of 6 pounds at _W_, but the hand will have to pull downward 6 feet at
_P_ in order to raise the load at _W_ 1 foot. If 8 pulleys were used,
a force equivalent to one eighth of the load would suffice to move
_W_, but this force would have to be exerted over a distance 8 times
as great as that through which _W_ was raised.

[Illustration: FIG. 111.--An effective arrangement of pulleys known as
block and tackle.]

163. Practical Application. In our childhood many of us saw with
wonder the appearance and disappearance of flags flying at the tops
of high masts, but observation soon taught us that the flags were
raised by pulleys. In tenements, where there is no yard for the family
washing, clothes often appear flapping in mid-air. This seems most
marvelous until we learn that the lines are pulled back and forth by
pulleys at the window and at a distant support. By means of pulleys,
awnings are raised and lowered, and the use of pulleys by furniture
movers, etc., is familiar to every wide-awake observer on the streets.

164. Wheel and Axle. The wheel and axle consists of a large wheel
and a small axle so fastened that they rotate together.

[Illustration: FIG. 112.--The wheel and axle.]

When the large wheel makes one revolution, _P_ falls a distance equal
to the circumference of the wheel. While _P_ moves downward, _W_
likewise moves, but its motion is upward, and the distance it moves is
small, being equal only to the circumference of the small axle. But a
small force at _P_ will sustain a larger force at _W_; if the
circumference of the large wheel is 40 inches, and that of the small
wheel 10 inches, a load of 100 at _W_ can be sustained by a force of
25 at _P_. The increase in force of the wheel and axle depends upon
the relative size of the two parts, that is, upon the circumference of
wheel as compared with circumference of axle, and since the ratio
between circumference and radius is constant, the ratio of the wheel
and axle combination is the ratio of the long radius to the short
radius.

For example, in a wheel and axle of radii 20 and 4, respectively, a
given weight at _P_ would balance 5 times as great a load at _W_.

165. Application. _Windlass, Cogwheels._ In the old-fashioned
windlass used in farming districts, the large wheel is replaced by a
handle which, when turned, describes a circle. Such an arrangement is
equivalent to wheel and axle (Fig. 112); the capstan used on shipboard
for raising