So deeply rooted was the erroneous notion that the air offered only an unappreciable resistance to moving balls, that the publication of Sir Isaac Newton's Principia, in which the resistance of the air in slow motions is ascer tained and confirmed by experiment, was not able to cor rect it. By extending the law for slow motions to those in which the velocity was very great, it was obvious that the resistance 'opposed to cannon balls was too great to be overlooked; though it did not amount, by the calculation, to that enormous degree which was afterwards dedcced from direct experiment. Newton has not attempted to in vestigate, in a direct manner, the path which a body will describe when projected into the atmosphere with a given velocity, and in a given direction. He spews, however, the particular state of density in the air, which will agree with the motion of a body in any curve whatever ; and, by the application of the principle to curves, which have some resemblance to the path of a projectile, he finds it differing little from what may be considered as the path of a body projected in our atmosphere. In the second edition of the Principia, which appeared in 1713, he corrects some of the oversights into which lie had formerly been led ; and he spews that a projectile, moving in a medium, whose density varies according to certain laws, and acted upon by a force directed to the centre of the earth, will describe an eccentric spiral, whose properties he describes.
The complete solution of this problem was not obtained, till Dr Keill challenged John Bernoulli to determine the curve described by a body projected through a medium resisting as the square of the velocity. The Swiss geo meter very soon gave a much more general solution than was demanded, independent of any limitation of the law of resistance, of the law of gravity, or of the law of den sity, provided that they were capable of being expi essed algebraically. Dr Brook Taylor gave a solution of the problem in its limited form.
In the year 169o, the celebrated Huygens published a treatise on Gravity, in which he endeavoured to prove, from a series of experiments, that projectiles discharged through the air with great velocity, described paths very different from a parabola. The inconsistency of the Gali lean theory, with the practice of artillery, was now par ticularly noticed by M. Ressons, a French artillery officer, who drew up a memoir on the subject, and presented it to the Academy of Sciences.* In this memoir, which was entitled Mithode pour tirer les bombes avec succes, he at tempts to show that the theory is of very little service in the use of mortars, and that the theoretical path of pro jectiles is justly described in the works of Blonde]; yet by directing mortars according to that theory, he could never obtain results that had the slightest agreement with it.
In the year 1736, a series of experiments was made at Woolwich, in order to determine the length of cannon that could enable them to shoot most efficaciously. These experiments were made with six 24 pounders, cast on pur pose and of the same weight, but varying in length from 8 feet to 101 feet. These pieces were all loaded alike,
with allotments of powder equal to half the weight of the bullet ; and five shot were fired from each, at an eleva tion of 74°. The following are the results which were obtained : Whether all the powder of the charge be fired ? 2d, Whether all the powder that is fired, be fired before the bullet is sensibly moved from its place ? And, idly, Whe ther the distance to which the Millet is thrown may not become greater or less, by changing the form of the cham ber, though the charge of powder and all other circum stances remain unchanged ? The committee, after nume rous experiments, found that all the powder was not fired; that the bullet was sensibly moved from its place, before all the powder that was fired had taken fire; and that a change in the form of the chamber would produce a change in the distance to which the bullet is thrown; the largest chamber of equal capacity always driving the ball farthest.t The committee, however, seem to have made some mis take ; for Mr Robins afterwards preyed, that the ball has not sensibly changed its place when the powder is fired.
Several experiments were about this time made in France on the ranges of cannon. M. St Remy has given us an account of a series made with pieces of cannon 10 feet in length, of the usual calibre, and elevated at an an gle of The following were his results, the quantity of powder being two-thirds of the weight of the bullet.
Pieces of the same calibre as the preceding, but some what shorter, had almost the same ranges when fired with only one half the former charge, or one-third of the weight of the ball in powder. See Remy's Memoirs of 4rtillery, vol. i. p. 69.
Another series of experiments was made at La Fere, in the year 1739, under the direction of the Chevalier de Borda. They were made with the usual pieces of all the preceding calibres, and were charged with various quan tities of powder, and elevated to 4°, to 15°, and to 45°. Experiments were also made with a 24 pounder, at dif ferent elevations, from 4 to and the following results were obtained with a charge of nine pounds of powder.
From the average range of these five shot, the effects of the different lengths were supposed to be deducible. The result of the experiments was, that the pieces of and 94 feet had the greatest range. Mr Robins has, how ever, shorn, that these experiments are by no means in consistent with his opinion, that the largest pieces ought to have the greatest Lange. The ranges with the 9 and 01 feet guns ought not to differ more than 35 yards from the ranges of the 8 and the 104 feet guns, according to his theory ; and yet with two subsequent trials with the 9 feet gun, the ranges differ no less than 650 yards ; and the average ranges made in these sticcessive days differ fi om each other 300 yards. Hence it is obvious, that these ex periments differ so much from each other, that they are not sufficient to decide the point for which they were un dertaken.