It remained for Robins, 1742, in a work then published, to show the real effect of the atmosphere upon moving bodies. He proved by actual experiment, that a 24lb. shot did not range the fifth part of the distance it should have done according to the parabolic theory. If a cannon shot moved in a parabolic curve, then from the known properties of that curve, it was evident that when fired with elevation, the angle of descent of the bullet should have been the same as the angle at which it was projected, and this he showed was not the case in practice. Now Robins acknowledged the opinion of Galileo, as regards the force of gravity, to be correct; he could not therefore attribute to him any miscalculation on the score of gravity. He therefore concluded, that the error of the “parabolic theory” arose from the supposition that the bullet continued to move at the same velocity throughout its course. ~Ballistic pendulum.~ Robins tried a series of experiments by firing at a ballistic pendulum at different distances; the oscillation of this pendulum enabled him to calculate the velocity of the bullet, at the time it struck the pendulum, and by this means he ascertained, that according to his expectations, the bullet moved slower in proportion as it became more distant from the point at which it was fired. This diminution he attributed to the resistance of the air. ~Trajectory more curved than a parabola.~ From these considerations it is evident that instead of moving over equal spaces A. C., C. D., D. E., (plate 22, fig. 4), at each succeeding second of time, it will require considerably longer to traverse each succeeding distance, and the force of gravity will consequently have longer time to act upon it, and will have the effect of lowering the bullet much more than it would do according to the “parabolic theory;” moreover it is evident, that as the velocity of the bullet diminishes, the trajectory or path followed by the bullet, will become still more incurvated. Having now proved the error of the “parabolic theory,” Robins began his endeavours to calculate the actual course of the bullet, according to this new theory which he had demonstrated, but this calculation was necessarily attended with great difficulties, for in so doing a number of circumstances had to be considered. ~Resultant.~ The resultant of the three forces acting on a projectile, (plate 23, fig. 1), viz., gunpowder, gravity, and the resistance of the air, is a motal force, diminishing in velocity at every instant, causing the projectile to describe a curved line in its flight, the incipient point of the curve lying in the axis of the bore of the piece, and its continuation diverging in the direction of the attraction of gravity, till the projectile obeys the latter force alone. EXPERIMENTS IN FRANCE. ~Angle for greatest range.~ ~Velocity.~