Oblong Bullets.—Are denominated by their diameter and weight. About 1600, when rifles began to be used as a military weapon, spherical bullets were fired; in the early part of the 18th century, however, it was found that good results could be obtained by the use of oblong projectiles of elliptical form. The great difficulty, however, of loading the rifle, which was ordinarily accomplished by the blows of a mallet on a stout iron ramrod, prevented it from being generally used in regular warfare. The foregoing plan was afterwards improved by making the projectile a little smaller than the bore, and wrapping it with a patch of cloth greased to diminish the friction in loading. The improvements which have been made in the last thirty years have entirely overcome this difficulty, and rifles are now almost universally employed, although until 1855 the mass of the American infantry was armed with smooth-bored muskets. The first person to overcome the difficulty of loading rifles was M. Delavigne, an officer of the French infantry. His plan, proposed in 1827, was to make the projectile small enough to enter the bore easily and to attach it to a sabot, which, when in position, rested upon the shoulder of a cylindrical chamber formed at the bottom of the bore to contain the powder. In this position the projectile was struck two or three times with the ramrod, which expanded the lead into the grooves of the barrel. The method of Delavigne was afterwards improved by Thouvenin and Minié, both officers of the French service. The projectiles suggested by them were elongated in form and the metal of the projectile was forced into the grooves of the rifling by means of a plug or cup driven into the base of the projectile, which was cast hollow for that purpose. The cup used in the Minié bullet wits made of sheet-iron. Mr. Greener of England appears to have been the first person to utilize this expanding or dilating action. Various other bullets have been invented, of greater or less usefulness, as the Whitworth, Pritchett or Enfield, and those used in the French, Austrian, and Swiss services. In the British service, the Enfield bullet is employed; this has a perfectly smooth exterior, and a conical boxwood plug inserted into a cavity at the base; they are made by machinery which draws in a coil of leaden rod, unwinds it, cuts it to the required length, stamps out the bullets with steel dies, drops them into boxes, and conveys them away.
United States Bullets.—The bullets used in the U. S. service are of two kinds, one for the rifle and carbine ball-cartridge weighing 405 grains, the other for the revolver cartridge weighing 230 grains. The metal used is an alloy of 16 parts of lead and 1 part of tin. The bullet in shape is a cylinder surmounted by a conical frustum terminating in a spherical segment. It has three rectangular cannelures which contain the lubricant. This latter is protected by the case which covers more than half the length of the bullet. A dished cavity is made in the base of the bullet to bring it to the proper weight.
Projectiles, Theory of. Is the investigation of the path, or [trajectory] as it is called, of a body which is projected into space. A body thus projected is acted upon by two forces, the force of projection, which, if acting alone, would carry the body onwards forever in the same direction and at the same rate; and the [force of gravity], which tends to draw the body downwards towards the earth. The force of projection acts only at the commencement of the body’s motion; the force of gravity, on the contrary, continues to act effectively during the whole time of the body’s motion, drawing it farther and farther from its original direction, and causing it to describe a curved path, which, if the body moved in a vacuum, would be accurately a parabola.
Trajectory in Vacuo.—This general theory is not the object of the present discussion, but simply the theory of projectiles as far as it relates to fire-arms. The path that the centre of gravity of a projectile would describe in vacuo would be a parabola, and the greatest range given by an angle of fire of 45°. Under the same angles of fire the range would be proportional to the squares of the velocities, the velocity least at the summit of the trajectory, and the velocities at the two points in which the trajectory cuts the horizontal plane equal. The time of flight would be given for an angle of 45° by the formula:
T = 1⁄4√X
In which T represents the time of flight, and X the range expressed in feet. These results are found to answer in practice for projectiles which experience slight resistance from the air, or for heavy projectiles moving with low velocities, as is usually the case with those of mortars and howitzers, for which, within certain limits, the above results are sufficiently accurate in practice.
Trajectory in Air.—A body moving in air experiences a resistance which diminishes the velocity with which it is animated. Thus it has been shown that certain cannon-balls do not range one-eighth as far in the air, as they would if they did not meet with this resistance to their motion, and small-arm projectiles which have but little mass are still more affected by it. This resistance is expressed by the formula:
P = ApR2 (1 + vr) v2;
in which P represents the resistance in the terms of the unit of weight, v the velocity, and pR2 the area of a cross-section of the projectile, A the resistance in pounds on a square foot of the cross-section of a projectile moving with a velocity of one foot, r is a linear quantity depending on the velocity of the projectile. For all service spherical projectiles A is .000514, and for all service velocities r is 1.427 feet; the value of A for the rifle-musket bullet is .000358; hence, the resistance of the air is about one-third less on the ogival than on the spherical form of projectile. A being a function of the density of air, its value depends on the temperature, pressure, and hygrometric condition. It has been demonstrated that the final velocity of a projectile falling in the air is directly proportional to the product of its diameter and density, and inversely proportional to the density of the air; the retarding effect of the air is less on the larger and denser projectiles, and for the same caliber an oblong projectile will be less retarded by the air than one of spherical form and consequently with an equal, perhaps less, initial velocity, its range will be greater. It has also been shown that great advantage in point of range is obtained by using large projectiles instead of small ones, solid projectiles instead of hollow ones, leaden projectiles instead of iron ones, and oblong projectiles instead of round ones. The ogival form, or the form of the present rifle-musket bullet, experiences less resistance in passing through the air than any other known. In consequence of the variable nature of the resistance of the air, it has been found impossible to find an accurate expression for the trajectory. Capt. Didion, of Metz, has, however, found an approximate solution; he states that all cases of the movement of a projectile may be divided into three classes: 1st. When the angle of projection is slight or does not exceed 3°, as in the ordinary fire of guns, howitzers, and small-arms,—for slight variations of the angle of projection above or below the horizontal, the form of the trajectory may be considered constant, and when the object is but slightly raised above or depressed below the horizontal plane, it may be considered as in this plane. 2d. When angles of projection do not exceed 10° or 15°, as in the ricochet fire of guns, howitzers, and mortars. 3d. When the angle of projection exceeds 15°, as is the case in mortar fire. For each of these cases he has deduced formulæ, by means of which the range, time of flight, etc., can be determined. As a projectile rises in the ascending branch of its trajectory, its velocity is diminished by the retarding effect of the air, and the force of gravity, in consequence of the resistance of the air alone, the velocity continues to diminish to a point a little beyond the summit of the trajectory, where it is a minimum, and from this point it increases, as it descends, under the influence of the force of gravity, until it becomes uniform, which event depends on the diameter and weight of the projectile, and the density of the air.
The inclination of the trajectory decreases from the origin to the summit, where it is nothing, it increases in the descending branch from the summit to its termination, and if the ground did not interpose an obstacle, it would become vertical at an infinite distance. An element of the trajectory in the descending branch has a greater inclination than the corresponding element of the ascending branch. Strictly speaking, therefore, the trajectory of a projectile in air is not a parabola, but is an exponential curve with two asymptotes, the first the axis of the piece, which is tangent to the trajectory when the initial velocity is infinite, the second a vertical line toward which the trajectory approaches, as the horizontal component of the velocity diminishes and the effect of the force of gravity increases. The curvature of the trajectory increases in the ascending branch to a point a little beyond the summit. The point of greatest curvature is situated nearer the summit than the point of minimum velocity. In the fire of mortar-shells, under great angles of projection, the trajectory may be considered as an arc, in which the angle of fall is slightly greater than the angle of projection. In the formulæ deduced by Didion, in consequence of considering the inclination of the trajectory as constant, the resistance of the air is slightly underestimated in the more inclined portions of the trajectory or at the beginning and end, and slightly overestimated in the less inclined portions or about the summit. It follows that the calculated trajectory will at first rise above the true one, then pass below it and again pass above it; the calculated ranges are therefore slightly in excess of the true ones.