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