Leaving the books of the practitioners, Robins had more to learn from the great circle of mathematicians who in the first part of the eighteenth century lent a lustre to European science. The old hypotheses were fast being discarded by them. Newton, in his _Principia_, had investigated the laws of resistance of bodies to motion through the air under gravity, by dropping balls from the cupola of St. Paul’s Cathedral; and he believed that the trajectory of a cannon ball differed from the parabola by but a small extent. The problem was at this time under general discussion on the Continent; and led to a collision between the English and the German mathematicians, Newton and Leibnitz being the two protagonists.[81] But, whatever the merits or outcome of the controversy, one thing seems certain. None of the great men of the day understood the very great accession of resistance which a fast-travelling body encountered in cleaving the air, or realized the extent to which the trajectory was affected by this opposing force. It was in fact universally believed and stated, that “_in the case of large shot of metal, whose weight many times surpasses that of air, and whose force is very great, the resistance of air is scarcely discernible, and as such may, in all computations concerning the ranges of great and weighty bombs, be very safely neglected_.”[82] In 1743 Robins’ _New Principles of Gunnery_ was read before the Royal Society. In a short but comprehensive paper which dealt with both internal and external ballistics, with the operation of the propellant in the gun and with the subsequent flight of the projectile, the author enunciated a series of propositions which, founded on known laws of physics and sustained by actual experiment, reduced to simple and calculable phenomena the mysteries and anomalies of the art of shooting with great guns. He showed the nature of the combustion of gunpowder, and how to measure the force of the elastic fluid derived from it. He showed, by a curve drawn with the gun axis as a base, the variation of pressure in the gun as the fluid expanded, and the work done on the ball thereby. Producing his ballistic pendulum he showed how, by firing a bullet of known weight into a pendulum of known weight, the velocity of impact could be directly ascertained. This was obviously a very important discovery. For an accurate measurement of the “muzzle velocity” of the bullet discharged from any given piece of ordnance was, and still is, the solution and key to many another problem in connection with it: for instance, the effect of such variable factors as the charge, the windage or the length of gun. In fact, as the author claimed, there followed from the theory thus set out a whole host of deductions of the greatest consequence to the world’s knowledge of gunnery. Then, following the projected bullet in its flight, he proceeded to tell of the continuous retardation to which it was subject owing to the air’s resistance.