An Eccentric Body, is one whose centre of figure does not correspond with the centre of gravity. MOTION OF A PROJECTILE. ~Modified by Gravity and air.~ If no force were acting upon the projectile, except the explosive force of gunpowder, it would by the first law of motion, move on for ever in the line in which it was discharged; this motion is modified by the action of two forces, viz., gravity and the resistance of the air. As the early cannons were of the rudest construction, and were used only to force open barriers, or to be employed against troops at a very short range, it was a matter of secondary consideration what course the bullet took, indeed it was generally believed, that it flew for some distance in a straight line, and then dropped suddenly. Acting upon this opinion we find that most of the early cannon had a large metal ring at the muzzle, so as to render it the same size as at the breech, and with such as were not of this construction they made use of a wooden foresight which tied on to the muzzle, so as to make the line of sight parallel to the axis, by which they conceived that they might aim more directly at the object which the bullet was designed to hit. ~Leonardo da Vinci, 1452.~ The first author who wrote professedly on the flight of a cannon shot was a celebrated Italian Mathematician, named Leonardo da Vinci, who explains his manner of studying phenomena, in order to arrive at safe conclusions, thus: “I will treat of the subject, but first of all I will make some experiments, because my intention is to quote experience, and then to show why bodies are found to act in a certain manner;” and taking as his motto, “Science belongs to the Captain, practice to the Soldier,” he boldly asks: “If a bombard throws various distances with various elevations, I ask in what part of its range will be the greatest angle of elevation?” The sole answer is a small drawing of three curves, (plate 20, fig. 3.), the greatest range being the curve about midway between the perpendicular and the horizontal. Yet this small drawing is very remarkable when we come to examine it. In the first place, we see that he recognises the fact that the trajectory is a curve throughout its length; secondly, that a shot fired perpendicularly will not fall again on the spot whence it was fired. Simple as they may seem, these two propositions recognise the force of gravity, resistance of the air, and the rotary motion of the earth. ~Tartaglia, 1537.~