falls 16 feet in the first second,
that in two seconds it falls 64 feet, and so on, in proportion to
the square of the time. So also will it be the case with a thrown
body, but the drop must be reckoned from its line of motion--the
straight line which, but for gravity, it would describe.

Thus a stone thrown from _O_ with the velocity _OA_ would in one
second find itself at _A_, in two seconds at _B_, in three seconds
at _C_, and so on, in accordance with the first law of motion, if
no force acted. But if gravity acts it will have fallen 16 feet by
the time it would have got to _A_, and so will find itself at _P_.
In two seconds it will be at _Q_, having fallen a vertical height
of 64 feet; in three seconds it will be at _R_, 144 feet below _C_;
and so on. Its actual path will be a curve, which in this case is a
parabola. (Fig. 57.)

If a cannon is pointed horizontally over a level plain, the cannon
ball will be just as much affected by gravity as if it were
dropped, and so will strike the plain at the same instant as
another which was simply dropped where it started. One ball may
have gone a mile and the other only dropped a hundred feet or so,
but the time needed by both for the vertical drop will be the same.
The horizontal motion of one is an extra, and is due to the powder.

As a matter of fact the path of a projectile in vacuo is only
approximately a parabola. It is instructive to remember that it is
really an ellipse with one focus very distant, but not at infinity.
One of its foci is the centre of the earth. A projectile is really
a minute satellite of the earth's, and in vacuo it accurately obeys
all Kepler's laws. It happens not to be able to complete its orbit,
because it was started inconveniently close to the earth, whose
bulk gets in its way; but in that respect the earth is to be
reckoned as a gratuitous obstruction, like a target, but a target
that differs from most targets in being hard to miss.

[Illustration: FIG. 58.]

Now consider circular motion in the same way, say a ball whirled
round by a string. (Fig. 58.)

Attending to the body at _O_, it is for an instant moving towards
_A_, and if no force acted it would get to _A_ in a time which for
brevity we may call a second. But a force, the pull of the string,
is cont