ASTRONOMY. 229 



of all the degrees of velocity, swift and slow, with which a 

 ball might be shot off, none would answer the purpose of 

 which we are speaking but what was nearly that of five 

 miles in a second.* If it were less than that, the body 

 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.t If 



* The moon describes in one second of time, nearly two thirds of a 

 a mile in its orbit round the earth ; and if its distance were diminished 

 it might still continue to revolve nearly in a circle round the same 

 centre, if its velocity were increased so as to compensate for the great- 

 er attraction, which would now draw it constantly out of the rectilinear 

 direction, in v^iiich it would otherwise move. This distance may be 

 supposed to be diminished till the moon is brought near to the earth's 

 surface, and it would, under these circumstances, still continue to com- 

 plete its revolution, if its velocity were increased to about five miles 

 in a second. Now for the description of such a revolution, there is no 

 difference between the moon and any other material substance at the same 

 distance ; for they would both be drawn down through the same space 

 in the same time by 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 acci- 

 dental circumstance) complete 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. 



t 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 direc- 

 tion 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 likewise prevent its completing its revolution 

 round the earth. Abstracting 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 project- 

 ed 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 motion of the projectile. Let us now conceive the 

 body to be projected back from C, with the velocity which it had ac- 

 quired 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 projection 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 v/hich they move must always pass through the earth's 

 centre ; and if the bodies rise on one side of this diameter, they must 



