Thus, after the theory of gunnery had exercised the genius of the learned for nearly two hundred years, and for almost fourscore of that time had rested on fundamentals which had never been contested, it was pronounced at once to be almost intirely useless, and that by one of the most competent judges. Now, whether it were owing to the deference due to the authority of that experienced artillerist, or to some other cause, I shall not determine, but observe, that it appears not from the history of the academy, that the sentiments of M. de Ressons were at this time controverted, or any reason offered afterwards for the failure of the theory of projectiles when applied to use. Nor can I pass unnoticed the pause that ensued before any further attempts were made to improve the theory of the art, either upon the old principles or upon new ones, except by such authors as seemed ignorant of this transaction, and who of course were not sufficiently apprized of the inefficacy of the properties of the parabola for directing practice. Or by those who were employed in speculatively investigating the nature of the curve traced by a ball in the air; a curve which began at last to be considered as one deviating much from the line of a parabola. Or, finally, by such as, having taken notice that Newton’s ideas had not been duly attended to, endeavoured to avail themselves of them, and of some experiments that had been made by others, for proving the great opposition of the air to bodies of swift motion; but without ascertaining the degree of that resistance, or enriching the art by any practical rules[20].
Such was the unhinged state of this part of the mixed mathematics, when within our memory Mr. Benjamin Robins took cognizance of it: nor could the subject have fallen into abler hands, endowed as he was by nature with a superior genius and unwearied application. Mr. Robins was deeply versed in geometry and the doctrine of numbers; but he knew the limits as well as the powers of both, and how insufficient they were for establishing any theory where matter was concerned, without preparing the way, by finding out the physical properties of that matter, by many and varied experiments and attentive observation. Those who had hitherto treated of the foundation of gunnery, by being too forward in the application of their mathematics, had in a manner hurt the credit of that admirable science. They ought to have seen the necessity of minutely examining every circumstance which could affect the course of a projectile, besides that of gravity. Mr. Robins perceived the error of his predecessors in that inquiry, and corrected it. Persuaded as he was from sir Isaac Newton’s Principia of the great resistance of the air to bodies moving in it, and also of the uncertainty of the force of gun-powder, and of the variations in the flight of shot, occasioned by the unavoidable varieties in the make of it, and in the make of the pieces of artillery which discharged it; apprized, I say, of so many causes of aberration, he justly concluded, that the foundation here was at least as much an affair of physics as of geometry, and that if the art of throwing bombs had not been advanced by theory, it was not because the art admitted of none, but because the theory which had hitherto been devised had been both defective and erroneous. He suspected that most of the writers on gunnery had been deceived, in supposing the resistance of the air to be inconsiderable, and thence asserting the track of all shot to be nearly in the curve of a parabola, by which means it came to pass that all their determinations, about the flight of projectiles of violent motion, had declined considerably from the truth. But in order to clear this point from every doubt, he found it necessary to ascertain the force of gun-powder, and by that step to estimate the velocity of the shot impelled by its explosion. That being done, he proceeded to measure the quickness of a musket-bullet, shot out of a given barrel, with a given quantity of powder; and to confirm the truth of his conclusions, he contrived a machine, by which the velocity of a bullet might be diminished in any given ratio, by being made to strike on a large body of a weight justly proportioned to it; whereby the swiftest motions, which otherwise would escape our examination, were to be exactly determined by these slower motions that had a given relation to them. The machine was a large wooden pendulum, which swung freely, but in so slow a manner, that its vibrations could easily be counted, whatever was the celerity of the bullet discharged against it. The thought was simple, ingenious, and incontestably his own.
He next inquired into the resistance made by the air to projectiles of rapid motion, and which he discovered to be much greater than had been supposed by any writer on the subject; and indeed so great, that it was manifest the curve described by any shot was very different from a parabola, and consequently that all the applications of the properties of that conic section to gunnery were so erroneous as to be totally useless. For by means of this pendulum, placed at different distances from the mouth of the piece, he clearly demonstrated how much a bullet, flying with a given velocity, would gradually lose of that motion by the opposition of the air: therein furnishing to the learned a signal and instructive instance of the fallacy of the most specious theories, that do not proceed hand in hand with experiments.
I should too much exceed the just bounds of a discourse of this kind, were I to enter more minutely into the system founded by Mr. Robins, confirmed and improved, as I find, by the labours of several of the learned in foreign parts of great celebrity[21]. I shall only add, that his performance well deserves the title he gives it of The new principles of gunnery, since the author may more properly be said to have invented a new science than to have added to an old one. And I believe I may venture to say, that no physico-mathematical disquisition hath done more honour to this country, or to the age, than the writings of Mr. Robins on this subject, which have been published, partly by this Society, partly by himself, and partly since his death (in the collection of his whole mathematical tracts) by his learned friend.
But though our worthy brother will ever be celebrated for being the inventor of the true principles of gunnery, yet it would be too flattering to his memory, to say he had carried the theory of this art to perfection. He himself was far from entertaining so high an opinion of his labours; nay he expressly declared, that he left some material points to be inquired into at more leisure (which other occupations and his immature death deprived him of) and he much regretted that he wanted conveniency and opportunities for making experiments on balls of a greater weight, than what he had used for ascertaining the initial velocity of them.
Much therefore are we indebted to Mr. Hutton, who, treading in the footsteps of the deceased, hath resumed and prosecuted this last desideratum, and hath shewn himself not unequal to so difficult an enterprize.
Mr. Robins, for determining the initial velocity of shot, arising from different quantities of powder, made use of balls of about an ounce weight; whereas Mr. Hutton, for the same purpose, hath employed those of different weights, from one pound to nearly three; or, in other words, Mr. Robins made trial with musket-shot only, Mr. Hutton with cannon-balls from 20 to about 50 times heavier. This was a considerable step gained in a disquisition of that part of the science, in which the resistance of the air and other circumstances were not concerned; and where neither analogy alone, nor mathematical deductions alone, nor the two combined, were sufficient for establishing principles applicable to the motion of cannon-balls, without making a new series of experiments: and with what labour and judgment these have been performed, you understood by the account which Mr. Hutton gave of them in his Paper.