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 continually drawing it towards _S_, and so it really finds itself at _P_, having described the circular arc _OP_, which may be considered to be compounded of, and analyzable into the rectilinear motion _OA_ and the drop _AP_. At _P_ it is for an instant moving towards _B_, and the same process therefore carries it to _Q_; in the third second it gets to _R_; and so on: always falling, so to speak, from its natural rectilinear path, towards the centre, but never getting any nearer to the centre.