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stroke is easily deduced from the chord of the arch, through which it ascends by the blow; for it is a well-known proposition, that all pendulous bodies ascend to the same height by their vibratory motion, as they would do if they were projected directly upwards from their lowest point with the same velocity they have in that point; wherefore, if the versed sine of the ascending arch be found (which is easily determined, from the chord and radius being given), this versed sine is the perpendicular height to which a body projected upwards with the velocity of the point of oscillation would arise; and consequently what that velocity is can be easily computed by the common theory of falling bodies.

“To determine the velocity with which the bullet impinged on the centre of the wood, when the chord of the arch described by the ascent of the pendulum, in consequence of the blow, was 174 inches as measured on the ribbon, no more is necessary than to multiply 34 by 505, and the resulting number (1641) will be the feet which the bullet would describe in l" if it moved with the velocity it had at the moment of its percussion. The velocity of the foot of the pendulum on which the bullet struck is determined to be 3 feet in 1" by the following calculation:-The distance of the ribbon from the axis of suspension being 71 inches, reduce 17 in the ratio of 71 to 66; the resulting number, which is nearly 16 inches, will be the chord of the arch through which the centre of the plate ascended after the strike: now, the versed sine of an arch whose chord is 16 inches and its radius 66 inches, is 1.93939; and the velocity which would carry a body to this height, or, which is the same thing, what a body would acquire by descending through this space, is nearly that of 3. feet in 1"."

Velocity, or its equivalent, penetration, is measured by English military authorities in a much more practical manner, but at the same time, in a way which is open to serious objections, as will be hereafter shown. Their machine is composed of a series of twenty elm planks half an inch thick, with an inch between them. These are made to slide into the grooves of a metal frame, and after being soaked in water, the rifles to be tried are fired at them from a distance usually of 200 yards, the penetration being estimated by the number of planks pierced. Three rounds are fired from each rifle, and the average of the three shots is taken to be the penetrating power of that particular rifle. The force of different kinds of gunpowder is estimated in the same way, using one rifle and similar bullets and charges of powder. The machine for private purposes may be made entirely of wood, and is then within the reach of every sportsman; but the elm boards of course require constant renewal as they are shot to pieces. In trying these experiments, the result should be recorded in a tabular form, as follows:

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Which will always give the result at one glance, without the necessity for a written description. In the military trials the amount of perforation, if any, in the last board is also expressed in tenths :- thus, first shot, 13.1; second shot, 12:4; third shot, 14:1-average, 13.2.

EPROUVETTES.

The above are the most correct modes of estimating the explosive force of powder, but the former is seldom used, on account of the complicated nature of the calculations required, and of the necessity for the impingement of the ball upon the proper centre of gravity of the pendulum. In common practice various contrivances, called eprouvettes, are employed. One of these consists of a small pistol with the muzzle closed by a valve, acted on by a spring. This valve is in connexion with a ratchet-wheel, which marks the extent to which it is opened by the explosion of the powder, but the spring varying in strength, the test is imperfect. The ordinary plan adopted by large sellers and purchasers is to load a small mortar with a given weight of powder, and then a ball, being accurately ground to fit it, in proportion to the strength of the powder will be the distance to which the ball is thrown. The eprouvette of the French Government is a small mortar capable of containing three ounces of powder, and this is expected to throw a copper ball of sixty pounds weight 300 feet. Sometimes the amount of recoil is made the test, and then a little mortar is suspended and loaded with ball, when the extent of the arc of the circle which it describes marks the strength of the powder.

RESISTANCE TO THE MOTION OF PROJECTILES THROUGH

THE AIR,

In a state of rest the air offers considerable resistance to the passage of balls and shot through it, and when moving in a direction different from that of the course of either, it is still more perceptible. It is calculated that this resistance increases nearly in a duplicate proportion to the velocity of the resisted body; that is, it is four times as much when the resisted body moves with twice the velocity; nine times as much when it moves with three times the velocity, and so on. In addition to this resistance there is also the force of gravity constantly tending to bring the body towards the centre of the earth.

ON RECOIL. The expansion of gunpowder when converted into gas being in all directions, it follows that at the moment of firing a blow is given to the breech end of the gun equal to that on the projectile which is to be moved. In proportion to the difficulty of moving the charge up the barrel will this force be continuously exerted, so that a large charge of powder exploded, with a light bullet in front of it, will exert less force upon the breech end of the gun, than a smaller charge of powder used to move a larger and heavier ball. So, also, the recoil varies with the same charge when the barrel is held horizontally, and when the muzzle is raised or depressed, being increased in the former position and diminished in the latter, in accordance with the laws of gravity. In shooting from the shoulder, the recoil is apparently increased still more than is really the case when the muzzle is pointed directly upwards, because the body cannot yield as it can do when the butt of the gun is held against the muscles of the chest and arm in a horizontal position. Again, in proportion to the weight of the whole piece will the recoil be affected, because a force which will move a body six pounds in weight readily enough will not have the same effect on one of nine pounds or more, having, in the language of science, to overcome a greater degree of vis inertiæ. Hold a heavy piece of wood or iron in the hand and a severe blow on it will not be felt, while the same, or even a much less force on a much lighter piece would occasion considerable punishment. This fact is well known to all those who have bad any experience with guns; and hence it has been considered necessary, independently of the question of safety, to have all guns made of sufficient weight to give the vis inertiæ required. It will be found that in proportion to the resistance offered by the shot or ball, and to the weight of the whole gun, and more especially at the breech, will be the recoil, but the former is not to be measured by its weight alone, being affected by the friction between it and the barrel. A highly polished surface has a tendency to diminish it, and, on the contrary, a rough one increases it. So, also, if the charge has to be driven through a smaller opening, as in barrels opened behind, the resistance is increased. Again, an ounce of lead causes a much greater amount of friction in proportion to the number of pellets into which it is divided, a single spherical ball producing the least, and dust-shot the most friction of all. On this subject I cannot do better than to give in extenso, as far as this point is concerned, a most interesting letter, by Mr. Boucher, which appeared in the Field on the 5th of June, 1858, in support of some previous statements of opinion made by me on the same side of the argument. He says:

Being one of those who deny that great recoil in the gun is any test whatever of great velocity in the shot, I beg to offer a few practical remarks in support of my opinion, drawn partly from lectures delivered by me at the United Service Institution previous to the report of your gun trials.

"In transcribing these remarks, I have little hope of being able to change the opinions of those who are wedded to other principles ; but, as the law of action and reaction seems to me to be misunderstood, or rather misapplied, by many with respect to fire-arms, I trust to be able to induce the unbiassed to re-examine the subject, and judge for themselves. I trust also to be able to show that my opinion is not at all incousistent with your idea of a model giin (Field, April 17)-namely, that it is one with which the greatest execution can be done upon the object shot at, without such a severe recoil as to make its use disagreeable to the sportsman.'

“* Gunpowder, when ignited,' says a high authority, 'expands with equal forces in every direction, and, consequently, it acts equally on the bottom of the bore and upon the ball during the passage of the latter along the cylinder, supposing it to fit tightly. Hence, neglecting the allowance which should be made for the frictions of the ball and the guncarriage, the velocity of the recoil will be to that of the shot inversely as the weight of the gun to that of the shot. Thus, supposing the initial velocity of a 24lb. shot to be 1600 feet per second, and the weight of the gun with its carriage to be 57.7 cwt., or 6462lbs., we shall have 5.9 feet per second for the velocity of the recoil.' The proportion,' says another military writer, “which the velocity of the recoil bears to that of the ball is inversely as their weights, due allowance being made for friction.'

“Such is the formula which is employed for computing, from the recoil, the velocity of the shot at the instant of its leaving the gun. This theory has been a recognised doctrine for more than a century. It is now spoken of as an

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