Part 1

A DISCOURSE ON THE _Theory of Gunnery_.

A DISCOURSE ON THE _Theory of Gunnery_.

DELIVERED AT THE Anniversary Meeting of the ROYAL SOCIETY, November 30, 1778.

By Sir JOHN PRINGLE Baronet.

PUBLISHED BY THEIR ORDER.

LONDON: PRINTED FOR THE ROYAL SOCIETY. MDCCLXXVIII.

GENTLEMEN,

Among the several experiments communicated to the society, during the course of the preceding year, none seeming so much to engage your attention, as those contained in the Paper, intituled, _The force of fired gun-powder, and the initial velocity of cannon-balls, determined by experiments_: with much pleasure therefore I acquaint you, that, on account of the pre-eminence of that communication, your Council have judged the author, Mr. CHARLES HUTTON, worthy of the honour of the annual medal, instituted on the bequest of Sir GODFREY COPLEY Baronet, for raising a laudable emulation among men of genius, in making experimental inquiries. But, as on former occasions, so now, your Council, waving their privilege of determining the choice, have acted only as a select number deputed by you, to prepare matters for your final decision. I come then, on their part, briefly to lay before you the state of the _Theory of Gunnery_, from its rise to the time when its true foundation was laid, in order to evince how conducive those experiments may be to the improvement of an art of public concern, as well as to the advancement of _natural knowledge_, the great object of your institution. And if, upon a review of the subject, you shall entertain no less favourable an opinion of Mr. HUTTON’s performance, than what your Council have done, it is their earnest request that you would enhance the value of this prize, by authorizing your President to present it to our ingenious brother in your name.

Artillery (in the large acceptation of the term) took place long before the invention of gun-powder. We trace the art to the remotest antiquity, since the Sacred Records acquaint us, that one of the kings of Judah, eight hundred years before the Christian æra, erected on the towers and bulwarks of Jerusalem engines of war, the contrivance of ingenious men, for shooting arrows and great stones for the defence of that city[1]. Such machines were afterwards known to the Greeks and Romans by the names of _balista_, _catapulta_ and others, which had amazing powers, and were not less terrible in their effects than the cannon and mortars of the moderns. It appears that the _balista_ was contrived to shower volleys of darts and arrows of a very large size upon the enemy, whilst the _catapulta_ or _onagra_ (as it was otherwise called) was fitted not only for that purpose, but for discharging stones of an enormous weight; I might say _rocks_, since some of them are reported to have weighed several hundred pounds. Batteries composed of numerous pieces of that kind of artillery, nothing could withstand. Yet, if we are rightly informed, their sole principle of motion consisted in the spring of a strongly-twisted cordage, made of animal substances singularly tough and elastic. These warlike instruments continued, not only during the time of the Roman empire, but to the 12th and 13th centuries, as we find from history; nor indeed is it probable that they were totally laid aside, till gun-powder and the modern ordnance, attaining a good degree of perfection, superseded their use. The very intelligent commentator of POLYBIUS[2] is of opinion, that the military art rather lost than gained by the exchange of the _catapulta_ for the mortar: but however that point may be determined in speculation, it is not likely that the ancient _tormenta militaria_ will ever be revived; but that all nations will keep to the art of gunnery and study how to improve it; that is, they will adhere to a system of artillery, wherein the moving power depends on the expansive force of gun-powder, or of some other substance of a similar nature.

Upon the first application of this principle to the purposes of war, nothing perhaps was less thought of than to assist so empirical a practice by scientific rules; for, however aiding in these matters the ancient mechanicians might have been, who, like ARCHIMEDES, had invented or perfected some of the _balistic_ machines, no praise seemed now due to the mathematicians for either the discovery or improvement of the new artillery. In fact, we find the practice of the art had subsisted about 200 years, before any geometer considered it as one that admitted a theory, or at least such a theory as was grounded on geometry.

It seems but just to trace and commemorate the inventors of the ingenious arts which furnish matter for discourses on these occasions; and not only the main inventors, but even those who first turned their thoughts upon the subject: for, though such men may not have produced any thing perfect, yet they may have suggested ideas to others of a less inventive, but of a more executive genius, and who, unprovided with those hints, would never have made any notable discovery. I must therefore observe, that the _Italians_ were the first who emerged out of those thick clouds of ignorance and barbarism which had so long overspread this quarter of the world. They profited by the unhappy fate of Constantinople; for by liberally receiving the learned emigrants on that distressful occasion, they were largely repaid by their arts and sciences, and still more abundantly by their language, whereby they were enabled to read and to translate those ancient manuscripts, which the Greeks had saved out of the wreck of their country. The art of printing, which was established soon after, was the means of quickly disseminating those treasures of knowledge, and concurred with the fall of the eastern empire to form an epoch for the advancement of learning, unparalleled in the annals of letters.

The end of the 15th century, and the whole of the 16th, were chiefly employed by the Italians in the study and in the translation of the old Greek authors. The geometry of the ancient Greeks, as well as the arithmetic in numbers and species of the Arabians, were cultivated; but both remained, as it were, sciences by themselves, unassisting to, or at best but weak and reluctant auxiliaries to the philosophy of the schools: and indeed how could the abstracted doctrines of numbers and quantities be strained to co-operate with a system, in which neither the laws of motion, nor any but the superficial, and often delusive properties of matter, were to be met with? The genius of the Greeks, all acute and brilliant as it was, had never been properly directed to the interpretation of nature, and was indeed unfit (as Lord Bacon pronounced) for a study that made so slow and painful a progress, by re-iterated and varied experiments and observations. It was no wonder then, if the _mixed mathematics_, as they are called, descended to the moderns in a state no-wise corresponding to the elegance and certainty of those parts of the science which were elementary and pure; and that those mixed parts should have been found defective and erroneous, in proportion (if I may so express myself) to the physical considerations that were to be taken into the inquiry. The imperfection of the ancients, with regard to natural philosophy, was not perceived at that time; nay, at the period we are treating of, the learned were firmly persuaded of the contrary, and that all that was wanting to be known concerning the laws of nature, and the properties of matter, was to be taken either directly, or by deduction, from the physics of ARISTOTLE. It was not till the 17th century was somewhat advanced, that men of science began to listen to Lord BACON and GALILEO, the great founders of the experimental and the true philosophy.

Mean while, in the beginning of the 16th century, unqualified as the Italians then were for entering upon physico-mathematical inquiries[3], they nevertheless made the attempt, and in particular took the theory of projectiles into consideration. Some imagined that a body impelled with violence, such as a ball discharged from a cannon, moved in a right line till the force was spent, and that then it fell in another right line perpendicularly to the earth. Upon this principle, absurd as it was, we find one of the earliest authors grounding his whole theory of gunnery[4]; whilst others, dissenting from his hypothesis, admitted only the straight line, in which the ball moved for some time after coming out of the piece, and that other straight line in which it fell to the ground; but asserted that these two were connected by a curve line, and that this curve was the segment of a circle. NICOLAS TARTAGLIA of Brescia, a mathematician of the first rank in those days, and still celebrated for his improvements in algebra, hath been supposed to be the author of this doctrine, no less erroneous than the former, and for which two of his books have been quoted[5]. Those I have never seen; but from another of his works, professedly written on this subject, and translated into English under the title of _Colloquies concerning the art of shooting in great and small pieces of artillery_[6], him I find, contrary to the opinion of his contemporaries, maintaining that no part of the track of a cannon-ball is in a right line, though the curvature in the first part of its flight be so small, that it needeth not to be attended to. But TARTAGLIA is far from supposing, that the line in question hath any relation to a _parabola_, or to any regular curve. It would seem then, that if this mathematician had at first been so far mistaken, as to fancy that some part of the course of a projectile was in a straight line, he had afterwards changed his opinion, and was perhaps singular in what he finally embraced.

From numerous instances one would imagine, that in those days, so far were men of science from making experiments themselves, that they even shut their eyes against what chance would have presented to their sight. For, whoever had minded the roving shot of an arrow, the flight of a stone from a sling, or had attended to a stream of water issuing from the spout of a cistern, might have been convinced, that the path of every projectile was in a continued curve, whatever little he otherwise knew concerning the properties of that one.

But had the observation of the philosophers gone so far, they had still been at a distance from the truth. They might have perceived a likeness between the track of those bodies in motion and a parabola, and concluded, from analogy, that all projectiles delineated that curve in the air; but they could never have realized their conjectures by mathematical demonstration, without previously knowing the law of _acceleration_ in falling bodies: a discovery reserved for the next century, and for GALILEO[7], one of the greatest ornaments of it.

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]._