Again, charging the same piece with equal quantities of powder, and balls of the same weight, and firing three times at the pendulum, placed at 25 feet dis tance from the mouth of the piece, the medium of the velocities with which the ball impinged was 1690 feet in 1". Then removing the piece 175 feet from the pen dulum, the velocity of the ball, at a me dium of five shots, was 1300 feet in 1". Whence the ball, in passing through 150 feet of air, lost a velocity of about 390 feet in and the resistance, computed fispm these numbers, comes out some thing more than in the preceding in stance, amounting to between 11 and 12 pounds avoirdupoise : whence, according to these experiments, the resisting power of the air to swift motions is greater than in slow ones, in a ratio which approaches nearer to the ratio of 3 to 1, than in the preceding experiments.
Having thus ascertained the resistance to a velocity of near 1700 feet in 1", he next proceeded to examine this resist ance in smaller velocities : the pendulum being placed at 25 feet distance, was fired at five times, and the mean velocity with which the ball impinged was 1180 feet in 1". Then removing the pendulum to the distance of 250 feet, the medium velocity of five shot at this distance, was 950 feet in 1"; whence the ball, in passing through 225 feet of air, lost a velocity of 230 feet in 1", and as it passed through that in terval in about of I", the resistance to the middle velocity will come out to be near 33i times the gravity of the ball, or 2/b. 10 oz. avoirdupoise. Now the resist
ance to the same velocity, according to the laws observed in slower motions, amounts to of the same quantity ; whence in a velocity of 1065 feet in (the medium of 1180 and 950) the resist ing power of the air is augmented in no greater proportion than of 11 to 7; where as in greater degrees of velocity, as before, it amounted very near the ratio of 3 to 1.
That this resisting power of the air to swift motions is very sensibly increased beyond what Sir Isaac's theory for slow motions makes it, seems hence to be evi dent. It being, as has been said, in mus ket, or cannon.shot, with their full charge of powder, nearly three times the quantity assigned by that theory.
The resistance of a bullet of three quarters of an inch diameter, moving in air with a velocity of 1670 feet in 1", amounting, as we said, to 10/b. the resist ance of a cannon ball of 24/b. fired with its full charge of powder, and thereby moving with a velocity of 1650 feet in 1", may hence be determined. For the velo city of the cannon ball being nearly the same as the musket-bullet, and its sur face above 54 times greater, it follows, that the resistance on the cannon ball will amount to more than 5401b. which is nearer 23 times its own weight. And from hence it appears how rash and erroneous the opinion of those is, who neglect the consideration of the resistance of the air as of no importance in the doctrine of projectiles. See Robins's Tracts ; Hut ton's Dictionary, article RESISTA.NCE.