Gunnery , the art of using guns, gunpowder, and projectiles. The forces which are of moment in gunnery as affecting the course of projectiles are terrestrial gravitation and the resistance of the air. The former is so nearly uniform, both in amount and direction, that it may be so regarded. But the difficulties which appear when we investigate the resistance of air are so formidable, that hitherto mathematicians have utterly failed to find a general formula, and have been obliged to resort to purely empirical methods. The first quantity to be sought is a unit of resistance with which all other degrees of resistance may be compared; and this is usually taken as the resistance offered by the air to a body having a front 1 foot square, moving 1 foot in 1 second. This quantity cannot bo determined theoretically, but it is found by careful trial that the value of this unit depends upon the form of the front, as well as its area. It is also considerably influenced by the shape of the rear. Hutton has given the following ratios between the values of the resistance:

Hemisphere, convex side foremost................. 119

Sphere........................................... 124

Cone, point foremost, with a vertical angle of 25° 42'. 126

Disk............................................. 285

Hemisphere, flat surface foremost.................. 289

Cone, base foremost............................... 291

In these ratios it appears that the resistance to the cone is about the same as that to a sphere, notwithstanding the sharp point of the former. From recent experiments by Prof. Bashforth of Woolwich, it also appears that the resistance to an elongated shot with a hemispherical front is less than that to a spherical shot of equal diameter, in the ratio of 1.845 to 1.531. Newton, in his Principia, gives as the front of least resistance a figure having nearly the section of a pointed Gothic arch. In practice it has been found that the "pointed ogive" or pointed Gothic arch gives less resistance than any other front hitherto experimented with. Investigators have therefore been compelled to determine the values of the unit independently for every kind of projectile in use. The dependence of resistance of air upon velocity is also determined experimentally. The latest and most trustworthy researches, by Prof. Francis Bashforth of the Woolwich artillery school, show that for velocities ranging from 1,400 to 1,700 ft. a second the resistance varies nearly as the square of the velocity; for those between 1,100 and 1,400 ft. it varies more nearly as the cube of the velocity; while for still lower velocities the ratio is in some power higher than the cube.

Thus a 15-inch shot, moving 1,500 ft. a second, encounters a resistance amounting to nearly a ton and a half, while a 10-inch shot encounters about three fourths of a ton at the same velocity. The amount of resistance offered by the air, and many other important data in gunnery, are ascertained by measuring the velocity of a projectile in different parts of its path. This is accomplished by means of an electro-veloci-meter. The projectile is made to break a series of electric circuits at several points, separated by equal intervals. The electric circuit passes through a machine, which contains a cylinder revolving at a known rate, and by appropriate devices the ruptures of the circuit make visible marks upon this cylinder. By measuring the distance between these marks, and multiplying it by the rate of revolution, the time which elapsed between any two instants of rupture becomes known. - Besides retardation, projectiles moving in air are subject to deviations resulting from their rotary motions about their axes. Spherical shot are always made of smaller diameter than the bore of the gun from which they are fired; the difference in the two diameters being termed windage.

One of its consequences is, that spherical shot are subject to a series of rebounds from side to side or from top to bottom of the bore, which is called balloting, and which causes them to leave the bore with a rotary motion. Let us suppose, for instance, that at the last ballot (rebound) the shot strikes the right side of the bore, as in fig. 1, receiving a rotary motion in the direction indicated by the arrows. This motion, combined with the motion of translation, tends to augment the pressure of the opposing air in the direction A I, and to diminish it in the direction A r; and the result is the deflection of the path of the shot to the right. Hence the effect of the last ballot in the case supposed is, first, to throw the shot to the left, while the unequal pressure of the air gradually deflects it back again to the right. If the final ballot were on the left side, the deflections would be reversed; if upon the top, the range would be slightly increased; and if upon the bottom, the range would be diminished. These effects were investigated, and the results demonstrated experimentally, by Magnus. They are much aggravated when, by reason of irregular density, the centre of gravity of a ball does not coincide with its centre of figure.

They are greater in small than in large projectiles for three reasons: 1. The actual amount of windage is very nearly the same for all calibres, and hence is relatively less for larger calibres than for small ones; therefore the balloting and consequent rotation will be less. 2. Large projectiles can be made more nearly isotropic than small ones, and the centres of figure and of gravity are more nearly coincident. 3. The effects of resistance of air are very nearly proportional to the surface exposed, i. e., to the square of the calibre; while the inertia of the shot and its consequent power to resist these effects is proportional to its mass, i. e., to the cube of the calibre. No projectiles have less lateral deviation than the largest round shot, whether the range be long or short; but the deviations of small spherical shot are notoriously great. In using elongated projectiles, the purpose is to reduce the total resistance encountered in passing through the air and through the target. This is attained by reducing the area of resistance, while the mass is not reduced. Less velocity is lost by them in consequence of the smaller front they offer to atmospheric resistance, as compared with spherical shot of equal weight.

After reaching the target they are required, in order to penetrate it, to make smaller holes than spherical projectiles of equal weight, and hence, with an equal striking velocity, will penetrate further. To secure these advantages, the elongated shot must always move with its axis as nearly as possible tangent to its path. But there are several causes which tend to make it rotate about its shortest axis, or tumble. To prevent this, and to give stability to the position of the long axis, a rotary motion about this axis is given to the projectile. This motion is totally distinct from the rotation of spherical projectiles just described, and the resulting effect of resistance of air is altogether peculiar. By reference to fig. 2 it will be seen that if the axis of the projectile were always parallel to its initial position, the curvature of the path would cause the resistance of air to act more and more upon the lower side, while the air upon the upper side would be rarefied in the wake of the projectile. The rotation upon the condensed air beneath causes it to roll to the right or left, according to the original direction of rotation; to which deflection the name drift is given. But in reality the axis does not continue parallel to its initial position.

It describes very slowly a conical surface, the apex of which is the centre of gravity of the shot; and what is most singular, the direction of this axial motion in pointed projectiles is opposite to that of flat-fronted projectiles. The conical rotation (or precession) of the axis causes an increased drift, the amount of which is even greater than the rolling drift already described. With pointed shot this deviation is to the right, but with flat-fronted shot to the left. The point of the former also droops, turning obliquely downward and to the right; the flat front turns obliquely upward and to the left. During the flight the former is more nearly tangent to the path than the latter. For uniform projectiles, the drift at moderate ranges is tolerably constant, and may be allowed for in sighting; but for round shot it is hopelessly irregular, sometimes to the right and sometimes to the left. At long ranges the drift of the elongated shot also becomes irregular, and often excessive, amounting sometimes to 200 or 300 yards to the right of the object sighted.

There are also vertical deviations, causing over-or under-shooting. In many cases these errors are more serious than lateral drift; for instance, against a battalion of troops, the hull of a vessel, the crest of a parapet, or the body of a deer, where the object is more extended laterally than vertically, and is more liable to be missed by vertical than by lateral error. There is another kind of error which may be called longitudinal deviation, or variation in range. A series of projectiles fired under conditions as nearly alike as practicable will differ in range; partly because no two charges of powder can be made to give exactly the same initial velocity, and partly because slight differences in the forms of the projectiles occasion marked differences in the amount of vertical drift. Hence the form of the trajectory is of great importance. To avoid vertical errors as much as practicable, it is desirable to give a high velocity to the shot; since the swifter its motion, the less curvature will gravitation produce in its path. It is evident that a low or flat trajectory is more dangerous to an enemy than a high one; but the former requires a higher velocity in the projectile than the latter.

The trajectories of spherical shot are at first less curved than those of elongated shot; but in the latter part of the flight, at considerable ranges, this relation is reversed. This is because the initial velocity of round shot is almost always greater, and the terminal velocity less, than that of elongated shot; the curvature everywhere being very nearly proportional to the velocity. The so-called "dangerous space" is that part of a projectile's path which is not higher above the earth than 5 ft. 10 in., or the stature of a man. The dangerous space is evidently greater at short than at long ranges, since it depends upon the angle which the descending branch of the trajectory makes with the earth, being greater the less the angle of descent; and the longer the range the greater is the angle of descent; for, to obtain the longer range, the muzzle of the gun must be more elevated, and the descending branch, owing to the resistance of the air, always makes a larger angle with the earth than the ascending branch. - The force of a projectile is measured by the product of its mass into the square of its velocity. The force, although a prime factor in the efficiency of a projectile, is not the only one; for cases may arise in which the energy is too great.

Thus in firing at a wooden vessel, a shot with a slow motion, making a large irregular hole, and hurling splinters, will be more destructive than a swift shot, cutting cleanly through, with comparatively little injury. In curved fire from mortars and howitzers, a low velocity is not only necessary, but desirable. Most of the effects of projectiles are accomplished by penetrating the objects against which they are directed, and their work will generally be most effectively accomplished when their energy is moderately in excess of that required for complete penetration. In this connection the penetration of iron vessels becomes of great interest and importance. - The most systematic experiments to ascertain the effect of shot on iron targets have been summarized by Capt. W. H. Noble of the English artillery, who deduces the following rules: 1. If two shot, having the same diameter and form of head, strike with equal energy, the penetration will be the same, though one may be a light round shot, striking with a high velocity, and the other a long heavy shot, with a low velocity. 2. A plate will be equally penetrated by shot of different diameters, provided this energy on striking is proportional to the diameter.

Thus, a 12-inch shot must have twice as much energy as a 6-inch shot, in order to penetrate the same plate. 3. The resistance of plates to penetration varies as the square of the thickness. These rules are subject to certain qualifications, depending upon the shape of the head of the shot. A hemispherical head is disadvantageous, because it tends to bulge laterally, and the same is partially true of a flat-fronted shot. The best form is the pointed ogive, which passes through without materially bulging, and makes a hole no larger than its true diameter. The flatfronted shot usually rips out a piece, called a button, in the shape of the frustum of a cone, the larger base being detached from the back of the plate. This is carried into the wooden backing, giving an increased resistance as compared with the ogive. Spherical projectiles are liable to flatten against the target and break in pieces. It is apparent that when flattening occurs the increased diameter involves the necessity of making a larger hole in order to penetrate. The striking velocity may be so great that the projectile will be dashed to pieces by its impact, and its energy partially absorbed in its own destruction, instead of that of the target.

This is especially true of spherical shot, fired with heavy charges at short range against thick plates. In comparing the effects of spherical and elongated projectiles against iron plates, many quantities must be considered, some favoring one form and some the other; but the final result is strongly in favor of the elongated form. For penetrating earth and battering masonry, similar considerations are applicable. - Concerning the effective range of guns, there is much popular misapprehension. To the scientific gunner the maximum range is of so little moment that its extent for common infantry bullets or for the heaviest seacoast projectiles is unknown. The longest range known to us was attained by one of Sir Joseph Whitworth's projectiles, viz., about 11,100 yards, not quite 6 1/2 miles. The efficiency is greatest near the muzzle, and diminishes as the range increases. A range may be considered effective at which there is a reasonable probability of doing injury. For bullets the effective range will depend upon the way in which the enemy's troops are deployed. Against a skirmish line it cannot much exceed 500 yards, but against massed troops it may be as great as 1,500 yards.

With field projectiles an enemy may be harassed at 2,500 yards, or even 3,000. In the bombardment of cities the extreme range is sometimes resorted to, on the assumption that a projectile falling anywhere within the line of fortification may work damage. Effective range turns upon the higher question of probabilities of fire. - Thus far we have discussed projectiles only, since their properties constitute the basis of gunnery. Gunpowder is merely the agent for giving them energy, and the gun for giving them direction. When we examine the relations among the three elements, the problem is highly complicated. We have two forces: the inertia of the shot, and the elastic force of the gases evolved by the powder. It is supposed that the metal contained in a given projectile is cast into a solid cylinder, having the diameter of the bore of the gun. Its length is called the column of metal of the projectile, and constitutes a measure of its inertia. Equal velocities will be imparted to different projectiles when the mean intensity of the forces acting upon them during a given time is proportional to their respective columns of metal.

But the intensity of the force of gunpowder is highly variable at different portions of the path along the bore, being very great near the seat of the shot, and rapidly declining toward the muzzle; hence equal, velocities will be imparted only when, at different points in the path along the bore, the respective intensities are proportional to the columns of metal. A complete analysis of the relations existing between the force of gunpowder and the motion of the shot in the gun, in terms of time, space, and mass, has never been attempted; it is a very formidable problem, and its chief difficulty is our ignorance of the rate at which the gases are developed and the quantity of heat evolved. But the greater the resistance opposed to the expansion of the gases of gunpowder, the more rapidly will the powder burn and develop gases, and the higher will be their temperature. Such an increased resistance is offered by an increased column of metal; and hence the conclusion that a longer column of metal carries with it the power of developing more force from a given quantity of powder than a shorter one.

On the other hand, the shorter column of metal will still have the higher velocity, though the longer will have the greater energy (mass multiplied into square of velocity); the difference in energy in favor of the latter being due to its greater mass, which more than compensates for its lower velocity. But if the quantity of powder is proportional to the column of metal, a larger charge will develop at every moment more gas than a smaller charge, and give a more intense force. But a larger charge occupies more space in the bore, and robs the projectile of a part of its travel, and hence of a part of the time in which it can receive acceleration. Increasing the charge will increase velocity up to a certain point, but beyond that point will diminish it. In small cannon the maximum pressure is probably reached before the shot has travelled three inches, and in large guns before it has travelled a foot. The time occupied by the shot in traversing the bore probably ranges from 1/90 to 1/200 of a second, and depends mainly upon the length of the bore and the quantity of powder.

A bold attempt was made by Rodman in 1858 to measure the distribution of the forces of gunpowder, by placing pressure gauges along the bore to register the pressure at different points; and to measure the time of passing over different parts of the bore, by a series of ruptures of electric circuits. (For a description of the pressure gauge, and the electric velocimeter, see Gunpowder, and Velocimeter.) It is obvious that an increase either in the column of metal or in the charge involves an increase in the intensity of the pressure of the gases, and hence an increased strain upon the gun. As the strength of a gun is limited, both the column of metal and the charge must be regulated accordingly. It is the maximum pressure which is dangerous. In large guns this difficulty is serious. Not only is a higher pressure produced by the longer column of metal, but the pressure is distributed over a larger area of bore, and the bursting tendency is in the ratio of the product of these two quantities. The greater thickness of walls gives increased resistance, but this increase is in a lower ratio than that of the bursting tendency, and hence large guns are relatively weaker than small ones.

To compensate for this difficulty, constructors have resorted to metals of greater strength, and especially have modified the action of the powder, so that the maximum pressures have been reduced, and the subsequent lower pressures have been increased. Thus the total effort of the powder upon the shot is undiminished. (See Gunpowder.) The column of metal of a spherical shot is two thirds its calibre; that of an elongated shot is usually between one and three fourths and twice its calibre. The latter limit has been found to be about as great as the strength of the gun will permit in large calibres. It is sometimes exceeded with very little advantage in the smaller and intermediate calibres. The charge of powder varies from one fourth to one tenth the weight of the projectile. With round shot it is sometimes as high as one third; but it is found that the velocity is not much increased when the charge is greater than one fourth. The velocities imparted to round shot vary from 1,400 to 1,750 ft. per second, and those of elongated shot from 1,150 to 1,500 ft. - For a good introduction to the science of gunnery, see "Ordnance and Gunnery," by Major J. G. Benton, U. S. A., and "Treatise on Artillery," by Lt. Col. C. II. Owen, R. A.

FIG. 1.

Fig. 2.