The next author who wrote on the flight of cannon shot was another celebrated Italian Mathematician, named Tartaglia. In the year 1537, and afterwards in 1546, he published several works relating to the theory of those motions, and although the then imperfect state of mechanics furnished him with very fallacious principles to proceed on, yet he was not altogether unsuccessful in his enquiries, for he determined (contrary to the opinion of practitioners) that no part of the track of a bullet was in a straight line, although he considered that the curvature in some cases was so little, as not to be attended to, comparing it to the surface of the sea, which, although it appears to be a plain, when practically considered, is yet undoubtedly incurvated round the centre of the earth. It was only by an accident he nearly stumbled upon one truth in the theory of projectiles, when he stated that the greatest range obtained by equal forces is at 45°. Calculating that at the angle 0° the trajectory was null, that by raising the trajectory, the range increased up to a certain point, afterwards diminished, and finally became null again when the projective force acted perpendicularly, he concluded that the greatest range must be a medium between these two points, and consequently at 45°. Others thought that a shot, on leaving the muzzle, described a straight line; that after a certain period its motion grew slower, and then that it described a curve, caused by the forces of projection and gravity; finally, that it fell perpendicularly. Tartaglia seems to have originated the notion that the part of the curve which joined the oblique line to the perpendicular, was the arc of a circle tangent to one and the other. ~Galileo, 1638.~ In the year 1638, Galileo, also an Italian, printed his dialogues, in which he was the first to describe the real effect of gravity on falling bodies; on these principles he determined, that the flight of a cannon shot, or of any other projectile, would be in the curve of a parabola, unless it was deviated from this track by the resistance of the air. A parabola is a figure formed by cutting a cone, with a plain parallel to the side of the cone. GRAVITY. ~Bullet as influenced by powder and gravity only.~ We will now proceed to consider the course of a bullet, as affected by _two_ forces only, viz., 1st. The velocity communicated to it by the explosion of the powder; and 2nd. By the force of Gravity. The attraction of the earth acts on all bodies in proportion to their quantities of matter. ~If no air, all bodies would fall in same time.~ ~Gold and dry leaf in same time.~