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.
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.