520. We have already seen, in the experiments of Fig. 68, that a body
projected horizontally describes a curved path on its way to the
ground, and we have to determine the geometrical nature of the curve.
As the movement is rapid, it is impossible to follow the projectile
with the eye so as to ascertain the shape of its path with accuracy; we
must therefore adopt a special contrivance, such as that represented in
Fig. 70.
B C is a quadrant of wood 2" thick; it contains a groove, along which
the ball B will run when released. A series of cardboard hoops are
properly placed on a black board, and the ball, when it leaves the
quadrant, will pass through all these hoops without touching any, and
finally fall into a basket placed to receive it. The quadrant must be
secured firmly, and the ball must always start from precisely the same
place. The hoops are easily adjusted by trial. Letting the ball run
down the quadrant two or three times, we can see how to place the first
hoop in its right position, and secure it by drawing pins; then by
a few more trials the next hoop is to be adjusted, and so on for the
whole eight.
521. The curved line from the bottom of the quadrant, which passes
through the centres of the hoops, is the path in which the ball moves;
this curve is a parabola, of which F is the focus and the line A A the
directrix.
[Illustration: FIG. 70.]
It is a property of the parabola that the distance of any point on the
curve from the focus is equal to its perpendicular distance from the
directrix. This is shown in the figure. For example, the dotted line F
D, drawn from F to the centre of the lowest hoop D, is equal in length
to the perpendicular D P let fall from D on the directrix A A.
522. The direction in which the ball is projected is in this case
horizontal, but, whatever be the direction of projection, the path is
a parabola. This can be proved mathematically as a deduction from the
theorem of Art. 515.
LECTURE XVI.
_INERTIA._
Inertia.—The Hammer.—The Storing of Energy.—The
Fly-wheel.—The Punching Machine.