226 
ASTRONOMY. 
would not get round at all, but would come to the ground, 
if it were in any considerable degree more than that, the 
body would take one of those eccentric courses, those long 
ellipses of which we have noticed the inconveniency.* If 
the velocity reached the rate of seven miles in a second, 
or went beyond that, the ball would fly off from the earth, 
and never be heard of more. In like manner with respect 
to the direction; out of the innumerable angles in which 
the ball might be sent off, (I mean angles formed with a 
line drawn to the centre,) none would serve but what was 
nearly a right one; out of the various directions in which 
the cannon might be pointed, upwards and downwards, 
every one would fail, but what was exactly or nearly hori- 
the force of attraction towards the earth’s centre; and therefore a cannon 
ball projected parallel to the horizon with this velocity would (if there 
were no resistance from the air or other accidental circumstance) com¬ 
plete its circular revolution, and come back to the place from which it 
had set out, in a few minutes less than an hour and a half, which is 
equivalent to the velocity of about five miles in a second.— Paxton. 
* The ball is supposed to be fired from a place not far from the earth’s 
surface, it can therefore be easily conceived that if its direction is much 
depressed below the horizon, it must be soon brought down to the ground; 
but it is not equally obvious that an elevation of any magnitude would 
ikewise prevent its completing its revolution round the earth. Abstract¬ 
ing from the air’s resistance, and of course omitting the supposition of a 
projectile force sufficient to carry the ball off into infinite space, it will 
move in the curve of an ellipse, of which one of the foci is situated in 
the centre of the earth. Now a body moving uninterruptedly in an 
ellipse must return in time to the same point from which it set out. The 
body therefore which, when projected from A, Fig. 6, PI. XXXIX, 
comes down to the earth at C, would have continued its course along 
the dotted line and returned to A, if the mass of matter in the earth had 
been collected together at its centre, so as not to interfere with the mo¬ 
tion of the projectile. Let us now conceive the body to be projected 
back from C, with the velocity which it had acquired in its fall, and 
with the direction in which it reached the earth, it would then pass 
through A, and come down on the other side of A I, in just the same 
curve, in which it had fallen from A to C. The same would apply to 
bodies projected upwards from B or D; and if the velocities of projec¬ 
tion were less or greater than what would have been acquired in falling 
from A, the bodies would still turn, but at some less or more distant 
point. The longest diameter, however, of the ellipsis in which they 
move must always pass through the earth’s centre, and if the bodies rise 
on one side of this diameter they must fall down on the other. Now it 
will be seen that the curves at B, C, and D, make the angles ABI, ACI, 
ADI less, as the body is supposed to go farther and farther befoie it falls, 
and that the curves, in which the body can complete a revolution near 
the surface, will in all its parts be nearly parallel to it. Hence ti e can¬ 
non ball fired upwards will come back again to the ground and not be 
able completely to go round the earth upon any other supposition except* 
ing that of its being fired in nearly an horizontal direction.— Paxton. 
