Various and numerous had been the disputes in Italy about the laws of motion in general, and especially about those of projectiles, from the time the mathematicians had begun the inquiry, till the publication of the dialogues of GALILEO on that subject (a space of upwards of a hundred years) but from that period, so evident did his demonstrations appear, that all contest ceased, and every man of science was convinced, that all projectiles moved in the track which he had discovered. For, as to the resistance of the air, which he had not passed unnoticed (as GALILEO himself had been the first, at least of the moderns, who started the notion of the weight of the air and the pressure of the atmosphere) yet so thin and so yielding did they esteem that fluid to be, that they were assured it could occasion no sensible, at least no material, deviation from that curve. As they had the principle from GALILEO, so they believed themselves warranted by that respectable author, not to fear from that cause any objection, which he himself had suggested, but had removed. _Among these projectiles_ (says he) _which we make use of, if they are of a heavy matter and a round form; nay if they are of a lighter matter, and have a cylindrical form, such as arrows shot from bows, their track or path will not sensibly decline from the curve of a parabola_[8]. Here then was the theory of gunnery laid, in appearance, on the most solid foundation. And thus far the Italians having proceeded, they seemed to have taken leave, and to commit the subject to other nations, whose greater power, or greater ambition, was more likely to make them avail themselves of the perfection of a military art, than their instructors. We had reason therefore to expect, that a neighbouring state, intent upon the advancement of the arts and sciences in general, would not fail to give particular attention to those that should appear most subservient to its grandeur. Accordingly we find, that our sister-society of that kingdom had not been many years established, when an ingenious member of that illustrious Body, not questioning the soundness of the Galilean principle in regard to projectiles, in the year 1677, proposed to the academy, as a problem for the improvement of artillery, how to direct a piece (suppose a mortar) so as to make the shot fall where one had a mind; or in the common expression, _to hit a mark_, the strength of the powder being given[9]. This thought met with general approbation, and so far were the academy from raising any difficulty about the obstruction which the air might occasion to a body moving with so much velocity in it, that we do not find the making experiments on that head was considered by them as an essential step to the solution; but that their principal geometers straightway set about solving the problem as it had been announced to them, some following one method, some another, and all upon the supposition of a projectile moving in the line of a parabola. But M.