TRACT 37.

OF GUNNERY.

283

that is, as —■ to 1 or gravity. Now, the velocity generated,or destroyed, by gravity, in describing the space s, is 8 */s,thus found, as vM6 : 32 : : a/s : 8 y/s-, and, when the spaceis the same, the velocities generated or destroyed, areas thesquare-roots of the forces, or the forces as the squares of thevelocities; and the velocity destroyed by the force in

3 f

describing the space s, being v -, therefore as 1: — d : : 64s : ;

hence 2d = eT/ Consequently /= f X and s =

Otherwise again.

2 f

144. Because the resistance is —, the gravity being 1,

therefore vv = — ~^s, and the fluents give v* = v 1 —

nd

and when v = 0, or the motion ceases, then v x —

Hence f — , and s = the same as the last.

J bgs 90s 7 96/

■

nd

6fg s

nd *

145. Hence it appears that the depth penetrated, is asthe density and diameter of the ball and the square of thevelocity, divided by the strength, or resisting force, of thematter of the obstacle. So that, if equal balls be dischargedagainst the obstacle, or block, then shall the depth of thecavities made by the balls be as the squares of their velocities;with which the experiments nearly agree.

146. Hence also it follows, that if unequal balls, but ofthe same density or matter, be discharged with equal velocityagainst an obstacle, the depths of the cavities will be pro-portional to the diameters of the balls: so that, a greater ballwill not only make a wider aperture, but will also penetratefarther into the obstacle, than a smaller ball, every othercircumstance being the same in both. Again, if it be known,from experiment, what is the depth of the cavity, which agiven ball, moving with a known velocity, makes in an ob-stacle, we can from that find the value of j, which denotesthe strength or firmness of the matter of which the obstacleconsists: and, in this manner, we may from experiments be