The experiments made by Dr Hutton in the years 1787, 1788, 1789, and 1791, were principally intended to ascer tain the resistance of the air to military projectiles. Balls of 2 inches, 2.78 inches, and 3.55 inches in diameter, were employed, to determine the resistance of very high veloci ties. They were discharged with velocities from 300 to 2000 feet per second, and were made to strike the pendu lum at several different distances from the guns. In all these experiments, the resistances varied nearly as the power of the velocity, the exponent being 2.028 for a ve locity of 200 feet per second, and increasing gradually to 2.136, which it reached when the velocity was 2000 feet per second.
In the year 1804, a new machine for measuring the initial velocity of projectiles was proposed and used by Col. Gro bert ; and a very favourable report of its accuracy was made to the National Institute of France, by Messrs Bos sut and Monge. The apparatus consists of a horizontal re volving axis, about 34 decimetres long, having at each of its extremities a circle or disc or pasteboard placed per pendicular to the axis. A rotatory motion is communicat ed to the axes, and consequently to the discs, by means of a weight suspended at the extremity of a rope, which, passing over a pulley 10 or 12 yards above the ground, coils itself about the arbour of a wheel and axle fixed at the same level as the discs. The motion given to the wheel and axle by the descent of the weight is communicated to the axis of the discs by an endless chain, passing round the wheel and axle, and also round a pulley on the axis of the discs. The instrument being thus constructed, let us sup pose that a ball traverses the two discs when in motion, in a direction parallel to their axes. It is obvious that the hole in each disc will not coincide with one another, and that the angular motion which the second disc has made while the ball was passing between them will be a measure •from which the velocity of the ball can be computed. Hence it is necessary to impress upon the discs an uniform and known velocity, and to measure accurately the arch passed over by the second disc during the transit of the ball from the one to the other. In the experiments which were made with this machine, the motion became sensibly uni form when the weight had arived nearly at the half of the vertical space which it traversed. The following is the for mula for calculating the velocity of the ball.
V=the velocity of the ball between the discs, consider ed as uniform ; T=3.141, the ratio of the circumference to the diameter of a circle; k=the ratio between the respective numbers of the turns made at the same time by the wheel of the axle, and the pulley of the axis of the discs, which in the following experiments was 1 7.875 (=the time employed by the wheel of the axle to make 71 number of turns ; 2—the distance of the hole made by the ball in the second disc from the axis of the discs; a=the arc passed over by that hole while the disc goes from the one to the other; b—the distance between the two discs.
The following experiments were made with a horse mus ketoon, 0.765 metres of interior length. The weight of the ball was 24.7 grammes, and it was projected with half its weight of powder. The mean velocity deduced from these experiments is 390.47 ; whereas the mean velocity found from experiments with the common infantry musket, 1.137 metre of interior length, was 428, exceeding the former in the ratio of 11 to 10. All the values of a are referred to that of 2=1 metre.
In order to afford the means of traversing the discs by throwing balls in different directions from 0° to 45°, Colonel Grobert gives to each disc a particular horizontal axis, to which a pulley is affixed ; and the rotatory motion is communicated by an endless chain to both axes, so that they may perform the same number of revolutions in the same period. The supporter of the second disc is capable of rising vertically, and fixing itself at different heights. The adjustment of this apparatus must, however, be attend ed with great difficulty.
On the Parabolic Theory of Gunnery:' Ix the process of our examination of the motions in the solar system, it appears that terrestrial gravity, or the heaviness of common sublunary bodies, is only a particular case of the mutual tendency of all matter towards all mat ter. It further appears, that a body on the surface of our globe gravitates in a line that is directed very nearly to the centre of the earth; and that the intensity of this gravitation is inversely proportional to the square of its distance from this centre.
Bodies let fall, or projected in any direction on the sur face of this earth, move under the influence of this force; and their motions may be computed from the general doc trines of dynamics, in the same manner as we computed the motions of the planets. They will either fall in the direc lion of gravity, or will rise in the opposite direction, or will describe a curve line concave toward the earth, which will be an ellipsis, parabola, hyperbola, or circle, according as the velocity and direction of the projection may have been combined But, in the greatest projections that we can make, the force of gravity is so nearly the same in every point of the path, that we may suppose it to be accurately so, without any sensible error, were it ten times greater than it is. Therefore in all disquisitions about projectiles, it would be useless affectation to embarrass ourselves with the varia tions. None of our projectiles rise a mile in the air, which is about of the mean radius of the earth, and will oc casion a diminution of gravity nearly equal to a quan tity altogether insignificant.