In the first experiments in ballistics by B. Robins, Count Rumford and Charles Hutton, the velocity of a projectile was found by means of the ballistic pendulum, in which the principle of momentum is applied in finding the velocity of a projectile (Principles of Gunnery, by Benjamin Robins, edited by Hutton, 1805, p. 84). It consisted of a pendulum of considerable weight, which was displaced from its position of rest by the impact of the bullet, the velocity of which was required. A modification of the ballistic pendulum was also employed by W. E. Metford (1824–1899) in his researches on different forms of rifling; the bob was made in the form of a long cylinder, weighing about 140 ℔, suspended with its axis horizontal from four wires at each end, all moving points being provided with knife edges. The true length of suspension was deduced from observations of the time of a complete small oscillation. The head of the pendulum was furnished with a wooden block, which caught the fragments of bullets fired at it, and its displacement was recorded by a rod moved by the bob (The Book of the Rifle, by the Hon. T. F. Fremantle, p. 336). An improved ballistic pendulum in which the geometric method of suspension is introduced has been used by A. Mallock, to determine the resistance of the air to bullets having a velocity up to 4500 F/S. (Proc. Roy. Soc., Nov. 1904). A ballistic pendulum, carried by a geometric suspension from five points, has also been employed by C. V. Boys in a research on the elasticity of golf balls, the displacement of the bob being recorded on a sheet of smoked glass. For further information on the dynamics of the subject see Text Book of Gunnery, 1897, p. 101.
In nearly all forms of chronographs in which the ballistic pendulum method is not used, the beginning and end of a period of time is recorded by means of some kind of electrically controlled mechanism; and in order that small fractions of a second may be measured, tuning-forks are employed, giving any convenient number of vibrations per second, a light style or scribing point, usually of aluminium, being attached to one of the legs of the tuning-fork. A trace of the vibration is made on a surface blackened with the deposit from the smoke of a lamp. Glazed paper is often employed when the velocity of the surface is slow, but when a high velocity of smoked surface is necessary, smoked glass offers far the least resistance to the movement of the scribing points. If the surface be cylindrical, thin sheet mica attached to it, and smoked, gives excellent results, and offers but little resistance to all the scribing points employed. The period of vibration of tuning-forks is determined by direct or indirect comparison with the mean solar second, taken from a standard clock, the rate of which is known from transit observations (“Recherches sur les vibrations d’un diapason étalon,” R. Koenig, Wied. Ann., 1880). In the celebrated ballistic experiments of the Rev. F. Bashforth, the time markings were made electrically from a standard clock, and fractions of a second were estimated by interpolation. Regnault (Mémoires de l’acad. des sciences, t. xxxvii.) employed both a standard clock and a tuning-fork in his determination of the velocity of sound. The effect of temperature on tuning-forks has been determined by Lord Rayleigh and Professor H. McLeod (Proc. Roy. Soc., 1880, 26, p. 162), who found the coefficient to be 0.00011 per degree C. between 9° C. and 27° C. The beginning and end of a time period is marked on a moving surface in many ways. Usually an electromagnetic stylus is employed, in which a scribing point suddenly moves when the electric circuit is broken by a projectile. Another method is to arrange the terminals of the secondary circuit of an induction coil, so that when the primary circuit is opened a small spark punctures or marks a moving surface (Helmholtz, Phil. Mag., 1853, p. 6). A photographic plate or film, moving in a dark chamber, is also used to receive markings produced by a beam of light interrupted by a small screen attached to an electromagnetic stylus, or by the legs of a tuning-fork, or by the mercury column of a capillary electrometer. In certain researches on the explosive wave of gases the light given by the burning gases made the time trace on a rapidly moving photographic film (H. B. Dixon, Phil. Trans., 1903, 200, p. 323). In physiological chronography the stylus is in many cases actuated directly by the piece of muscle to which it is attached; when the muscle is stimulated its contraction moves the stylus on the moving surface of the myograph (M. Foster, Text Book of Physiology, 1879, p. 39).
Gun Chronographs.—Probably the earliest forms of chronographs, not based on the ballistic pendulum method, are due to Colonel Grobert, 1804, and Colonel Dabooz, 1818, both officers of the French army. In the instrument by Grobert two Grobert and Dabooz.large disks, attached to the same axle 13 ft. apart, were rapidly rotated; the shot pierced each disk, the angle between two holes giving the time of flight of the ball, when the angular velocity of the disks was known. In the instrument by Colonel Dabooz a cord passing over two light pulleys, one close to the gun, the other at a given distance from it, was stretched by a weight at the gun end and by a heavy screen at the other end. Behind this screen there was a fixed screen. The shot cut the cord and liberated the screen, which was perforated during its fall. The height of fall was measured by superposing the hole in the moving screen upon that in the fixed one. This gave the approximate time of flight of the shot over a given distance, and hence its velocity.
In the early form of chronoscope invented by Sir C. Wheatstone in 1840 the period of time was measured by means of a species of clock, driven by a weight; the dial pointer was started and stopped by the action of an electromagnet which moved a Wheatstone.pawl engaging with a toothed wheel fixed on the axle to which the dial pointer was attached. The instrument applied to the determination of the velocity of shot is described thus by Wheatstone:—“A wooden ring embraced the mouth of the gun, and a wire connected the opposite sides of the ring. At a proper distance the target was erected, and so arranged that the least motion given to it would establish a permanent contact between two metal points. One of the extremities of the wire of the electromagnet (before mentioned) was attached to one pole of a small battery; to the other extremity of the electromagnet were attached two wires, one of which communicated with the contact piece of the target, and the other with one of the ends of the wire stretched across the mouth of the gun; from the other extremity of the voltaic battery two wires were taken, one of which came to the contact piece of the target, and the other to the opposite extremity of the wire across the mouth of the gun. Before the firing of the gun a continuous circuit existed, including the gun wire; when the target was struck the second circuit was completed; but during the passage of the projectile both circuits were interrupted, and the duration of this interruption was indicated by the chronoscope.”Professor Joseph Henry (Journal Franklin Inst., 1886) employed a cylinder driven by clockwork, making ten revolutions per second. The surface was divided into 100 equal parts, each equal to 1 second. The time marks were made by two galvanometer Henry.needles, when successive screens were broken by a shot. Henry also used an induction-coil spark to make the cylinder, the primary of the coil being in circuit with a battery and screen. This form of chronograph is in many respects similar to the instrument of Konstantinoff, which was constructed by L. F. C. Breguet and has been sometimes attributed to him (Comptes rendus, 1845). This chronograph consisted of a cylinder 1 metre in circumference and 0.36 metre long, driven by clockwork, the rotation being regulated by a governor provided with wings. A small carriage geared to the wheelwork traversed its length, carrying electromagnetic signals. The electric chronograph signal usually consists of a small armature (furnished with a style which marks a moving surface) moving in front of an electromagnet, the armature being suddenly pulled off the poles of the electromagnet by a spring when the circuit is broken (Journal of Physiology, ix. 408). The signals in Breguet’s instrument were in a circuit, including the screens and batteries of a gun range. The measurement of time depended on the
- The velocity of the projectile is found thus. Let V be the velocity of the bob, due to the impact of the projectile, v the velocity of the projectile, h the height through which the bob is raised
h = V2 , and V = √. 2g
If W be the weight of the bob, and w the weight of the projectile, then
wv = (W + w)V, and v = ( W + 1) √ . w
If l be the true length of suspension, and C the length of the chord of the arc of displacement of the bob after being struck, then
C2 = 2hl, and v = ( W + 1) √ g . C. w l
Also if T be the time of a complete small oscillation of the pendulum,
2π = √ g , T l so that v = ( W + 1) 2πC . w T