without changing the relations between the tra-
jectory and its chord.
The Line of Sight is the line passing through 'the sights of the piece and the point aimed at. The Line of Departure is the prolongation of the axis of the bore at the instant the projectile leaves the gun; or it is the tangent to the tra- jectory at the muzzle.
The Plane of Sight, sometimes called the plane of fire, is the vertical plane containing the line of sight.
The Plane of Departure is the vertical plane containing the line of departure.
The Angle of Departure is the angle made by the line of departure with the horizontal plane.
The A7igle of Elevation is the angle made by the axis of the bore with the horizontal plane when the piece is laid.
The Jump is the difference between the angle of elevation and the angle of departure.
Drift is the departure of the projectile from the plane of fire due to the resistance of the air and the rotation of the projectile.
Muzzle Velocity is the velocity of the pro- jectile on leaving the piece.
Remaining Velocity is the velocity at a given point of the trajectory.
Striking Velocity is the remaining velocity at the target.
The Horizontal Range is the horizontal dis- tance from the muzzle of the gun to that point of the descending branch of the trajectory (point of fall) which is at the level of the gun. Ordinarily the term range means the distance between the gun and the target.
The Angle of Fall is tlie angle that the tangent to the trajectory at the point of fall makes with the horizontal plane passing through the muzzle.
The Striking Angle is the angle made by the tangent with the horizontal plane at the strik- ingpoint.
The Dangerous Space is the horizontal dis- tance over which an object of a given height will be struck.
Direct Fire is with high velocities and angles of elevation not exceeding about 20 degrees.
Curved Fire is with low velocities and angles of elevation not exceeding about 20 degrees. High Angle Fire is when the angle of eleva- tion exceeds 20 degrees.
Indirect Fire is when the target is invisible from the firing-point.
History. The theories relative to the motion of projectiles were originally of the crudest kind. Up to the middle of the Sixteenth Cen- tury bullets were supposed to move in right lines from the gun to the target, and shells fired from mortars were thought to describe a path made up of two right lines joined by an arc of a circle. The trajectory was divided into three parts: First, violent, which was thought to be a right line; second, middle or mixed, which was an are of a circle; and third, the natural, which was a right line. In a work on gunnery, published by Niceolo Tartaglia, a Venetian, in 1537, he proved that no part of the path of a projectile could be a right line, and that the greater the velocity of the pro- jectile the flatter is the path of the projectile. In his calculations, he considered the resist- ance of the air, and found that an angle of 45 degrees gives the maximum range. Tartaglia also invented the gunner's quadrant (q.v.) for giving elevations. Galileo demonstrated the parabolic form of the trajectory in ihicuo in his Dialogues on Motion. Newton's discovery of the law of gravitation made plain the cause of the curvilinear motion of projectiles. By the use of the calculus, his own invention, he determined the momentum transferred from the projectile to the particles of air at rest, which is the method followed at the present day, and which leads to the law of the square of velocity. So far as a rigorous solution of the trajectory in air is concerned, the problem remains to-day about where Newton and Jean Bernouilli left it.
Ballistic Machines. There are two ways in which the velocity of a projectile may be determined experimentall}- — by measuring the ]irojectile's momentum, and by actually measur- ing the time required for the projectile to pass over a given space. The first method is the older; and many years ago, when guns and pro- jectiles were small and velocities were low-, the results were sufficiently accurate for practical purposes. Modern gunnery is much indebted to the now discarded ballistic pendulum and gun pendulum, which have long since been sup- planted by the cheaper and more accurate ma- chines using the second method.
The Ballistic Pendulum was invented about 1740, by Benjamin Robins, who was the first to make a ststematic and intelligent series of experiments to determine the velocity of projectiles. The u-hirling-machine, for determining the resistance of the air to slowly moving bodies of different forms, is also attributed to Robins. The principle of the ballistic pendulum, as well as of Count Rumford's gun-pciululum, is the transformation of the elements of the momentum of the small mass and high velocity of the projectile to the more easily measured large mass and low velocity of the pendulum. The original ballistic pendulum of Robins consisted of a block of wood bolted to a plate of iron, the whole revolving freely about a horizontal axis, the block, when struck by a bullet, recoiling through a certain arc, which was measured by the length of ribbon wound off the reel. This light pendulum could stand the impact of mus- ket-balls only, but with it Robins began the science of gunnery by determining the relations which should exist between the calibre, length of barrel, and charge of powder. Dr. Hutton (1775-91), Dr. Gregory (1814), and Major (later Colonel) Mordecai. of the United States Ordnance Department (1842-45), made many experiments with improved ballistic pendulums.
Major Mordecai used, also, the gun-pendu- lum, his apparatus being briefly as follows: A ballistic pendulum weighing 9358 pounds, with a cast-iron block made in the shape of a hollow frustrum of a cone, with hemispherical bottom and filled with sand-bags, to receive the pro- jectiles, which were from 6 to 32 pounds in weight. By very delicate bearings and meajis of mounting, this pendulum, if set in motion through an arc of 12 degrees, would come to rest only after 30 hours. The recoil was meas- ured by a sliding pointer on a brass line. In front of this pendulum was constructed a screen of 2-inch plank, designed to intercept the blast from the discharge, a 12-inch circular aperture being left for the passage of the pro-
