A discourse on the theory of gunnery / Delivered at the anniversary meeting of the Royal Society, November 30, 1778

by Sir John Pringle

It was he who first investigated the effects of gravity on falling bodies, and upon that foundation demonstrated, that all projectiles would move in a parabola in a non-resisting medium. And as he made little account of the resistance of the air, whose properties were then imperfectly known, he proved that a ball shot horizontally would, in its flight, describe half a parabola; and when the piece had an elevation above the horizon, the ball would describe a whole parabola, supposing it to fall on the plane of the battery. By the same method of reasoning he shewed, that whatever the ranges of the projected body, or the elevations of the piece were, the ball would still trace that curve line, of a greater or lesser amplitude, by the time it descended to the level of the place from whence it came.

Thus far went Galileo, confining his projections to the horizontal plane of the battery; but Torricelli his disciple soon after carried the theory farther, by tracing the shot to its fall, whether that place was above or below the plane; and still found, by geometrical deductions, that it flew in a parabola of a larger or a smaller amplitude, according to the angle of elevation of the piece, and the strength of the powder.

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. Blondel, who had been the proposer, and who more particularly had studied the question, composed a large volume on the subject, which he published a few years after[10], under the title of L’Art de jetter les Bombes; a performance much celebrated at the time, and that continued in no small request long after, as containing, besides his own, the labours of several other members of that society of the most distinguished merit. So many, and such hands concurring in framing this work, it was no wonder that the learned throughout Europe were confirmed by it in the Galilean theory; and the more as M. Blondel had obviated the only objection they supposed could be made to it, the resistance of the air, which he had taken care expressly to mention, and so to combat as to persuade the reader, that the retardation arising from that cause was so inconsiderable as to be of no account in the practice.

This illusion about the small or non-resistance of the air to bodies rapidly moving in it, was so prevalent at the end of the last century, and in the beginning of the present, that in the history of the Royal Academy for the year 1707, we find their worthy and most accomplished secretary, after taking notice of the joint labours of so many able mathematicians concerned in Blondel’s publication, venturing to say, it did not appear that any thing was then wanting for the practice of the art [of Gunnery] except perhaps perfecting the instruments for pointing a cannon or mortar ... but that geometry had done its part, so to speak, with regard to practice. &c.[11]

But far be it from our intention to relate the imperfections of others, in order to raise ourselves by the comparison. Candour requires of us not only to acknowledge, that in this country, as to the point in question, we did not surpass our neighbours; but ingenuously to own that, on the contrary, we were perhaps more liable to exception. For, some years before Blondel’s work appeared[12], a treatise was published by one of our own artillerists, Anderson (a person of eminence in his profession) intituled The genuine use and effects of the gun, in which the author strenuously supports the Galilean theory; nor do we learn he was ever contradicted among us, although he undertook to answer all those who should make objections to it. Nay, when he had an opportunity afterwards of making experiments on the ranges of bombs, and by those trials was assured that their flight was not in a parabola; yet so far was he from ascribing the deviation from that figure to the resistance of the air, that he had recourse to an hypothesis, repugnant to all the laws of motion, to salve appearances, and to reconcile those experiments with his former doctrine[13].

And did not Dr. Halley, so long the ornament of this society, communicate in the year 1686 a Paper, which he calls A discourse concerning gravity, in which, treating of the motion of projectiles, he says, that being aware of the deflexion from the parabolic curve that might be occasioned by the resistance of the air, he had made some experiments, even with cannon-balls, to estimate the force of that resistance; yet conclude, That in large shot of metal, whose weight many thousand times surpassed that of air, and whose force is very great, in proportion to the surface wherewith they press thereupon, this opposition was not discernible. And again, Though in small and light shot, the opposition of the air ought and must be accounted for; yet in shooting great and weighty bombs, there need be very tittle allowance made; and so these rules [those, to wit, grounded on the principle of Galileo] may be put in practice to all intents and purposes, as if this impediment [the resistance of the air] were absolutely removed[14]. Such conclusions, which we now find to be erroneous, were the less to be expected from so eminent a person, as they argued too much haste to finish a theory, that was to be made subservient to present use.

It might indeed have been expected, that men of science applying themselves to this study, would have been sooner awakened to the consideration of the great opposition of the air, by the Principia of Newton, published a little after this Paper of Halley’s[15]. For in that excellent work the illustrious author had demonstrated, that the curve described by a projectile, in a strongly resisting medium, differed much from a parabola, and that the resistance of the air was great enough to make the difference between the curve of projection of heavy bodies and a parabola far from being insensible, and therefore too considerable to be neglected.

Have we not then less to plead for not attending to the Principia of Newton in this article[16], than the mathematicians of other nations, who, as M. de Fontenelle observes[17], partly from the difficulty of understanding that concise and profound work, and partly from a misapprehension of its tendency (which they fancied was to revive the exploded doctrine of occult qualities) were late in becoming acquainted with it? But it is not so easy to account for their inattention to Huygens, a known and even then a much esteemed author, and who indeed was second to Newton alone in science and in genius. For he in the year 1690 had published a treatise on Gravity, written in a popular manner, wherein he gave an account of some experiments he had made at Paris, and in the academy, by which, as well as by mathematical investigations, he was convinced of the truth of Newton’s conclusions, in regard to the great opposition of the air to bodies moving swiftly in it; and, by consequence, believed that the track of all projectiles was very different from the line of a parabola[18].

But excepting Newton and Huygens, the learned seemed universally to acquiesce in the justness and sufficiency of the principles of gunnery invented by Galileo, enlarged by Torricelli, confirmed and reduced to system by Anderson, Blondel, Halley and others; and so far were the theorists, in that branch of science, from suspecting any defect or fallacy in these principles, that they seemed rather to reproach the practical artillerists, for not profiting more by the instructions which they had so liberally imparted to them. Nor do we find that an apology was made for the empirical exercise of the art, by any author of note in that line, earlier than the sixteenth year of this century, when M. de Ressons, a French officer of artillery, distinguished by the number of sieges at which he had served, by his high military rank, and by his abilities in his profession; when he, I say, thus qualified to bear testimony, presented a memoire to the Royal Academy (of which he was a member) importing, that although it was agreed that theory joined to practice did constitute the perfection of every art, yet experience had taught him, that theory was of very little service in the use of mortars. That the work of M. Blondel had justly enough described the several parabolic lines, according to the different degrees of the elevation of the piece; but that practice had convinced him there was no theory in the effects of gun-powder: for that having endeavoured, with the greatest precision, to point a mortar agreeably to those calculations, he had never been able to establish any solid foundation upon them[19].