Theory of Gunnery.— Instruments of great precision, mechanical construction of much accuracy, and a considerable knowledge of the higher mathematics are necessary to obtain and make use of trustworthy data for the establishment of sound principles on which to base the theory of gunnery. It is therefore not surprising that, owing to the early discovery of gunpowder, the art was long practised in a rude manner, without any attempt being made to reduce it to a science. Thus, though firearms appear to have been in use from the early part of the 14th century, little of value was understood of the laws regulating the flight of projectiles till the time of Nicholas Tartaglia, who published a treatise on the subject at Venice in 1537. About sixty years before that date, Leonardo da Vinci had enunciated some of the mathematical principles of trajectories in a manner which shows him to have possessed far more insight than any of his contemporaries; but he did not pursue the inquiry, and Tartaglia may be regarded as the father of ballistics. He was a man of great talent and ingenuity, but unfortunately had no opportunities of observing artillery practice; he was unable, therefore, to bring his calculations and speculations to the test of fact, and failed to carry conviction to the minds of the philosophers of the age. Before his time it had been generally believed that a ball on leaving the bore of a gun proceeded for some distance in a straight path,—a fallacy which lurks in the phrase “point-blank,” not yet expunged from popular speech. He saw, however, that “a piece of artillery cannot shoot one pace in a right line,” and propounded the axiom that “the more swifter a pellet doth flie, the lesse crooked is his range,”—a truth expressed at the present day by the statement that a high velocity gives a flat trajectory. This eminent philosopher claimed the invention of the gunner’s quadrant; he took into account in his calculations the resistance of the air, but placed the angle of elevation at which the maximum range would be obtained at 45°, which would only be the case in vacuo. Galileo was the next mathematician of note who investigated the subject. In his Dialogues on Motion, published in 1638, he recognized fully the resistance of the air, and pushed on the inquiry in the direction indicated by Tartaglia. It was not, however, till Newton’s time that a substantial basis was laid down for a true theory of gunnery. The grand discovery of the law of gravitation revealed the hitherto unguessed secret of the projectile’s fall to earth. The great improvements in mathematical methods of analysis invented by him rendered possible solutions of previously impracticable problems; while the splendour of his achievements in natural science stimulated philosophers of all countries. Towards the end of the 17th century he investigated the trajectory of a projectile on the supposition that the resistance of the air varied as the first power of the velocity. Bernoulli in 1718 gave a solution of the problem, on the supposition that the resistance varied as any given power of the velocity. This solution was, however, left in such a complicated state that no practical use can be made of it. No further progress was made till Benjamin Robins in 1742 published his Hew Principles of Gunnery, in which he furnishes a notable example of the manner in which theory should be wedded to practice, and hypothesis to experiment. Had Robins been in the possession of accurate instruments he would probably have arrived at results of considerable correctness. He invented the ballistic pendulum, and was the first to ascertain experimentally with any degree of correctness the velocities of projectiles on leaving a gun. A “triangle” or gyn supported a pendulum of iron having a massive wooden bob; to the bob was fixed a steel ribbon which passed through a steel clamp set to the desired pressure. A bullet fired into the wooden bob caused the pendulum to swing; the length of the arc described was recorded by the steel ribbon; the weight of the bullet and the conditions of oscillation of the pendulum being known, the velocity of the bullet could be calculated from the length of the arc. The weight of Robins’s first pendulum was 56 B), and it was therefore only suited for small arms. It could measure the velocity at only one point each round, and therefore, to ascertain the velocity lost by a ball in passing through the air, it was necessary to fire a series of rounds at one distance, and afterwards a similar series of rounds at another distance, Velocities of 1700 feet per second were measured, and the loss of velocity due to the resistance of the air, up to a distance of 250 feet from the muzzle, was approximately ascertained. Robins discovered that the resistance of the air was greatly increased as soon as the ball travelled faster than sound, and attributed it to the creation of a vacuum behind the shot, into which the air could not rush with speed greater than that of sound. Count Rumford in 1751 made use of the recoil to measure the velocities of bullets, on the principle that the momentum of the bullet forward was equal to the momentum of the gun backward. To carry this out, the gun was suspended as a pendulum, and the length of the arc it described on firing measured. By firing a bullet from a gun thus suspended into the ballistic pendulum, two independent records were obtained, and it would have been easy to calculate the lυs3 of velocity, from the muzzle to any range at which the pendulum could be hit, by the combination. The roughness of the methods unfortunately did not permit completely satisfactory results. Dr Hutton next took up the inquiry, and increased the weight of the pendulum and the bullets. No very great advance, however, seems to have been made till 1840, when experiments on the resistance of the air to the motion of spherical shot were carried on at ^Metz by the French Government. MM. Piobert, Morin, and Didion were the chief experimenters. They raised the weight of the receiving pendulum to nearly 6 tons, and fired into it 50-pound balls at a range of 330 feet. The information now obtained spread over a much wider field than that traversed by Robins. It was even found possible to construct the trajectories of projectiles with some approach to truth, and empirical formulae were laid down by which ranges and times of flight could be approximately calculated. It was not, however, till the introduction of electricity as a means of determining the velocities of projectiles that accurate knowledge of the resistance of the air was obtained. In 1840 Professor Wheatstone invented an instrument for this purpose, called the electromagnetic chronoscope. He has had many successors, whose productions exhibit a great amount of ingenuity; those from which the most valuable results have been obtained, and which are in use at the present moment, are the Bashforth chronograph, the Noble chronoscope, the Le Boulengé chronograph, and the Watkin chronograph.

The general principle on which these four instruments are designed is that a projectile after leaving the gun shall sever a fine wire stretched acros3 a screen, thus breaking an electric current, and causing a record to be made by the instrument at the moment. The Le Boulengé is connected with two wire screens only, the others with several. As two records are necessary to obtain a velocity, reading the time taken by the shot to pass between two screens, the number of points of a shot’s flight at which an instrument is capable of indicating the velocity is one less than the number of screens employed. The chronograph invented by the Rev. F. Bashforth, late professor of mathematics to the Advanced Class of the Royal Artillery, is shown in fig. 1.

A is a fly-wheal, which, in revolving, carries with it K, a cylinder covered with paper specially prepared to receive the records of the clock and screen. B is a toothed wheel which turns the drum M and unwinds the string CD, thus allowing the platform S to descend slowly down the slide L. E, E' are two electromagnets, whose keepers are supported by the frames d, d'; f,f are the ends of springs which act against the attraction of the electromagnets. There are two distinct currents—one through the screens and E, the other through the clock and E'. When these are interrupted, one by the shot cutting a screen, or the other by the clock beating seconds, so that the magnetism is destroyed, the spring/or/'carries back its keeper, which, by means of the arm a or α', gives a blow to the lever b or b', causing the marker m or m' to depart from the uniform spiral it has been describing—a spiral consisting of a double line running round the cylinder. The apparatuses adjusted so that the platform L, and consequently the markers rn, m', descend about ⅜ inch for each revolution of the cylinder; the folds of the spiral are thus I inch apart. The cylinder is made to revolve with considerable rapidity, so that the intervals between the successive clock marks indicating seconds measure from 20 to 25 inches; hence the screen marks indicating the moment of the severance of the wire by the shot can be allotted to their proper value in seconds with great accuracy. The screens are so contrived that the current, interrupted by the passage of the shot through one, is completed again before the next is reached. To accomplish this, the cutting of the wire is made to release a spring which makes a fresh contact; thus any number of screens can be used and a corresponding number of records obtained.

The chronoscope invented by Captain Noble of Elswick, late Royal Artillery (figs. 2, 3, 4), is constructed to furnish eight or more records, according to the number of discs, and is so excellently adapted for the measurement of exceedingly minute portions of time that it is usually employed to ascertain the velocity acquired by the shot in moving from a state of rest inside the gun at different parts of the bore. It is thus intimately connected with gunmaking, but, having the same character as other velocity instrument's, is described here. The screens used for recording the flight of the shot through the air are now discarded, and the

“cutting plugs,” shown in figs. 5, 6, 7, are substituted for them. In figs. 5 and 6 B is the bore, and A a flat-headed shot or cylinder passing along it in the* direction of the arrow. The plugs are screwed into the sides of the gun, as in fig. 7, which gives an end view of the bore. As

; the shot passes, its foremost edge pushes up the knife D, cutting the wire e, which passes in at one side of the plug C, then through a hole in the knife D, and out again at the other side of the plug. The ends of this wire are connected with the main wires leading to the instrument, and the knife D, in cutting it, interrupts the current. Fig. 4 shows a 10-inch gun pierced to receive cutting plugs in eighteen places. The main wires run from a plug to the primary of a Ruhmkorff coil, fig. ∙2, near the instrument, with which the secondary communicates. Figs. 2 and 3 show the instrument in plan and elevation.

A, A are disks, 36 inches in circumference, fixed on a horizontal shaft S. This shaft is caused to rotate, so that the edge of the disks travel at about 1100 inches per second, by a series of toothed wheels F, F, gearing as shown, and worked into rapid motion by the handle C. This motion is kept up with regularity by the descent of the weight B acting on the hindmost shaft, the speed of which is multiplied 200 times at the shaft S. At V is a vernier, reading a graduated circle, which is fixed on the shaft S. The edges of the disks are covered with a coating of lampblack. One of the secondary wires G is brought from the coil, and placed in communication with the revolving disk; the other secondary wire H is fixed in a discharger Y, just clear of the edge of the disk. A stop-clock is placed on a stand D, and records the rate of revolution of one of the shafts. When the gun is fired the shot begins to move, and, as it travels along the bore, cuts the wires of the plugs in succession, breaking the primary currents, and causing sparks to pass in the secondary current from the dischargers Y, Y, to the disks A, A, which are in rapid revolution. The sparks burn off the lampblack and record their positions on the disks by a minute spot. Now if the shot could cut all the plug-wires simultaneously, all the spots on the disks would be in a straight line, but it does not do so, and during the intervals between the cutting of successive plug-wires the disks continue to rotate, so that the line of spots forms a spiral round the cylinder represented by the disks, as is apparent on bringing the machine to rest. The shaft S is then turned so as to place each spot in succession opposite an index, and the spaces travelled by the circumferences of the disks between the spots are read off on the graduated circle. As the circumference of the disks is made to travel at the rate of 1100 inches per second, and the vernier reads to thousandths of an inch, the machine indicates portions of time rather less than a millionth of a second; it is, in fact, practically correct to hundred-thousandths of a second. A millionth is about the same fractiou of a second as a second is of a fortnight. Thus the distance between two successi ze spots gives the actual time occupied by the shot in moving over the portion of the bore between two corresponding successive plugs, and therefore the velocity acquired at some point of this travel. As the increment of velocity is constantly decreasing after the charge is fairly lighted, the point at which the measured velocity is acquired is very slightly behind the middle of the space between the two plugs. The observations are worked out, accidental errors eliminated, and the results put in the form shown in column 3 of Table I.

The “crusher gauge” (fig. 8) is so closely associated in its use with the Noble chronoscope that it is convenient· to give a description of it here, though its indications are valuable to the gunmaker rather than to the gunner. In fig. 4 are shown three plugs, A, B, and C, driven through the walls of the gun, and terminating flush with the bore. These plugs contain gauges for measuring directly the pressure of the gas on the surface of the bore. They are of the same diameter as the cutting plugs, and can be used in any of the twenty-one holes pierced in the gun. Fig. 8 shows the construction. The bottom of the plug is chambered out, and a steel anvil E is placed at the top of the chamber. Against’ this anvil is pressed a cylinder of pure copper A, carefully tested for quality, which is held in its place by a spring B. A piston C fits accurately the lower part of the chamber, any ingress of gas being prevented by the gas-check D, which is flush with the bore. When the gun is fired the powder-gas presses the piston hard against the copper cylinder A, which yields and becomes shorter, expanding laterally. The plug is then removed from the gun, and the nozzle unscrewed; the cylinder is extracted and measured. Its compression is compared with those given in a table constructed from experiment, and the pressure of the gas per square inch recorded. With the chronoscope the velocities are obtained directly from the time shown by the instrument to have been taken by the shot in passing over the interval between two cutter plugs. From these velocities calculation deduces the pressures required to produce the increments of velocity. These calculated pressures are compared with and confirmed by those obtained directly from the indications of the crusher gauge. Table I. shows the nature of the information obtained from Table I. [table]

the combination of the two instruments, when used with a 38-ton gun, firing an 800-K> projectile, with 130 lb of 1 ’ 5-inch cubical powder.

The last velocity is calculated from that taken by a Le Boulengé instrument outside the gun. This chronograph, the invention of an officer of the Belgian artillery, is shown in figs. 9, 10, and its mode of application in fig. 11.

The shot, after leaving the gun, cuts the wire of the first screen, and subsequently the wire of the second screen. The wire of the first screen conveys a current through an electromagnet A (figs. 9, 10), which then supports a cylindrical rod C. This rod is sheathed with a zinc tube D, which is renewed from time to time as required; several short zinc tubes are slipped on, instead of one long one, if no great variation in the velocities is expected, so as to save material. Directly the first screen is cut, the rod C, which is called the chronometer, drops. The wire of the second screen conveys a current through another electromagnet B, which supports a much shorter rod F, called the registrar. The shot, in cutting the second screen, releases this short rod, which falls on a disk 0, setting free a spring Μ. This spring carries a horizontal knife N, which flies forward and nicks the zinc tube covering the long rod. The nick made by the knife, if released while the long rod is still suspended, is the zero point. The currents from both screens pass through a disjunctor by which they can be cut simul taneously. When this is done the long and the short rods fall at the same moment. A certain time is consumed by the short rod in reaching the disk, setting free the spring, and cutting a nick on the zinc. During this time the long rod is falling into a recess in the stand, deep enough to receive its full length. The instrument is so adjusted that the nick thus made is 4 - 435 inches above the zero point, corresponding to0∙15sec. This is the disjunctor reading, and requires to be frequently corrected during experiments unless the weather is exceptionally favourable to the electrical conditions. Instead now of using the disjunctor to cut both currents simultaneously, suppose the shot to cut them in succession; then the long rod will be falling for a certain time, while the shot is travelling from one screen to the other, before the short rod is released. The longer the shot takes to travel this distance, the farther the long rod falls, and the higher up on it will be the nick made by the knife. A simple calculation connects the distance fallen through by the rod with the time occupied by the shot in travelling over the distance between the screens, and hence its velocity at the middle point is known. A graduated rule is generally supplied with each instrument, arranged for a certain distance between the screens; from this any velocity obtained can be read off at once.

The electric chronograph, invented by Captain Watkin, R.A. is shown in figs. 12, 13, 14.

Two brass cylinders A, A revolve on pivots B, B, C, C. Between them, at the top, hangs a brass weight (fig. 13), suspended freely by means of a piece of steel B, which pivots in another piece A let into the base of the weight. Two arms E enter, on falling, two V springs on the bed of the instrument, which catch the weight, A finely-pointed brass wire, CD, enclosed through part of its length in an ebonite tube, passes through the upper end of the weight from side to side; the piece B of the weight is placed between the ends A, C of the lever arms of the holder (fig. 14). The arm CD pivots on the pin F; AB is fixed. K, K is an electromagnet; on its keeper H is fixed a strong spring· G, G. When this spring is...