Part 22

The subject of fire-arms embraces a very wide ground, as will appear if we consider the many different forms in which these weapons are constructed in order best to serve particular purposes. Pertaining to this subject, attention must also be directed to the modern projectiles and to the newer explosives that have largely taken the place of ordinary gunpowder. The shot gun, fowling-piece, and sporting rifle properly come under the head of fire-arms, and in the march of improvement these forms have most commonly been in advance of military muskets and rifles, the ingenuity bestowed on all their details being worthy of admiration. Nevertheless it is to the implements of war that general interest attaches; for on them depends so much the fate of battles and the destiny of nations, that whenever any country is engaged in war the question of arms becomes one of surpassing importance, enlisting the patriotic instincts of every citizen. Hence in the following pages our space will be devoted mainly to weapons of war, and more particularly to those that have been adopted by our own country.

Everyone of course is aware that guns, cannon, and gunpowder are by no means inventions of the nineteenth century; but there are fewer acquainted with the fact that rifling, breech-loading, machine guns, and revolvers were all invented and tried hundreds of years before. The devices by which some of these ideas were sought to be realised in past ages appear to us in some instances very primitive, not to say childish, when compared with modern work: but it must be remembered that nearly all the appliances required for producing such weapons had themselves to wait for their invention until the nineteenth century; such, for instance, as the steam-hammer, powerful and accurate tools, refined measuring implements, material entirely reliable such as the new steel, and also scientific investigations of all the conditions involved. The military fire-arms are of so many different forms and patterns that we can deal here with but a selection from the various services. If a rough classification had to be made, the most obvious distinction would be between the weapons the soldier carries in his hands (small-arms) and those which are mounted on some kind of carriage and discharge projectiles of much greater weight (ordnance). Ordnance again includes guns mounted on forts, carried in ships, or taken with an army into the field, in each case coming into action under different conditions. Partaking somewhat of the nature of both field-guns and of small-arms are the machine guns, of which the French mitrailleur was the first example, afterwards developing into much more effective weapons in the hands of Gatling, Gardner, Nordenfelt, Maxim, and Hotchkiss.

As much will have to be said about _rifling_ the bores of muskets and cannon, we may here explain the nature and object of this device. The projectiles used in all guns down to comparatively recent times were almost invariably of spherical form, and could indeed scarcely be otherwise with smooth-bore weapons. As the diameter of the shot would necessarily be something less than that of the bore of the barrel, a considerable loss of power would result from the escape of the powder gases between the shot and the barrel, which escape is known as _windage_. Another disadvantage of the spherical projectile is that for the same weight of metal the air offers a greater resistance to its passage, and consequently checks its speed more quickly than that of any other circular form; for the air resistance is proportional to the square of the diameter, and therefore if we take a ball of 1 in. diameter and a cylinder of 1 in. in length, each having the same weight of metal, the diameter of the cylindrical shot will be a little more than four-fifths of an inch, and the air resistance to the ball will be exactly half as much again as to the cylinder, that is, in the proportion of 3 to 2. Again, the passage of the spherical shot within the barrel of the gun will not be in a straight line, but in a series of rebounds from side to side, and its direction on leaving the muzzle will depend upon which part of the bore it just before impinges on, as from that it will also take a rotatory “twist” that will in part determine its path through the air.

Now if an elongated projectile were fired from a smooth-bore gun, its course through the air would be erratic to a degree impossible to the spherical shot, for it would turn end over end with deviations that would make aiming impracticable. But if the elongated projectile is made to spin rapidly enough about its longitudinal axis, it flies through the air quite steadily, the axis of rotation remaining parallel to that of the gun throughout the whole flight. The steadiness due to rapid rotation has familiar examples in spinning tops, in gyroscopic tops, in the way arrows are feathered so that the air may cause them to revolve axially, and so on. The axial rotation of the projectile is effected by ploughing out in the cylindrical barrel of the gun a number of spiral or twisting grooves, which the projectile is compelled to follow as it travels along the barrel, either by means of corresponding protuberances formed upon its surface in the first instance, as in Jacob’s bullets, or by studs let into it, as in the studded shots and shells for ordnance which constituted at one time the regulation plan adopted by the British Government; or otherwise by making the force of the explosion expand some portion of the projectile in such a manner that this portion shall completely fill up the grooves, thus preventing windage, and causing the projectile to follow the twist of the grooves. This is the more general method, especially since the adoption of breech-loading. The Lancaster rifling, and that advocated by Whitworth, are the same in principle, but differ in appearance, from the section of the barrel being made in the one case oval, in the other hexagonal or polygonal, but with the twist necessary to produce rotation.

Incident to the discharge of all fire-arms, great and small, is a phenomenon of which we have to speak, because it is one which in the mounting of heavy ordnance especially has to be taken into account. And as it also illustrates in a very direct way one of the most general laws of nature, while people often have very vague and erroneous ideas of its cause and operation, it deserves the reader’s attention. In gunnery it is called the _recoil_, and is familiar to anyone who has ever fired a pistol, fowling-piece, or rifle, in the kick backwards felt at the moment of the discharge. This law is in operation whenever the condition of a body in respect to its rest or motion is changing. That is, whenever a body at rest has motion given to, or if when already moving it is made to go faster or slower, or to stop, or when the direction of the motion is changed from that in a straight line. Now although these changes or actions are frequently occurring before our eyes, the operation in them of Newton’s third law of motion does not generally present itself to common observation. This third law was stated by Sir Isaac Newton thus:—“To every action there is always an opposite and equal reaction.” Now the expanding gases due to the gunpowder explosion press the bullet forwards and the barrel (with its attachments) backwards, with the same pressure in both cases, but at the end of the bullet’s passage along the bore the same velocity is not imparted to the two bodies, because the same pressure acting for the same time on bodies of unequal _mass_ always produces velocities that are inversely proportional to the _masses_. The reader should try to acquire this conception of _mass_, remarking that it is a something quite distinct from that of _weight_. A given lump of metal, for instance, would have exactly the same _mass_ in any part of the universe, whereas its weight would depend upon its position; as, for instance, at the distance from the earth of the moon’s orbit, it would _weigh_ only as 1/3600th part of its weight at the earth’s surface, and if it could be carried to the very centre of the earth it would there have no weight at all. Though the lump of metal will have different weights at different parts of the earth’s surface, it has been found (by experiment) that the weights of bodies at any one place are proportional to their masses. Therefore the same numbers that express the weights of bodies might also express their masses; but for certain good reasons these quantities are referred to different units. In England a piece of metal weighing 32 lbs. under standard conditions is said to have mass = 1; and so on. As with the _same pressure acting for the same time_, the velocities imparted are inversely proportional to the masses, it follows that the number expressing the velocity multiplied by that representing the mass in each such case of action and reaction will give the same product, or in other words the _amount of motion_ (momentum) will be the same. This is what Newton meant by saying the reaction is _equal_ to the action. We may now by way of illustration calculate the velocity of recoil of a rifle under conditions similar to those that might occur in practice. Let us suppose that the rifle, including the stock and all attachments, weighs 10 lbs., and that from it is fired a bullet weighing one-sixteenth of a pound, with a velocity at the muzzle of 1,200 ft. per second. To obtain the amount of motion or the momentum, we should here multiply the number expressing the _mass_ of the bullet by 1,200, but for our present purpose the weight numbers may be used for the sake of simplicity; therefore 1/16 x 1,200 = 75 will represent (proportionately) the forward momentum of the bullet, and according to Newton’s law the backward momentum of the rifle will be, on the same scale, 75 also. We must therefore find the number which multiplied by 10 will give 75, and this obviously is 7·5. That is as much as to say that at the instant the bullet is leaving the muzzle, the rifle itself, _if free to move_, would be moving backward at the speed of 7½ ft. per second. Observe that this result would be the same if the rifle were fired where weight is non-existent; nor is the recoil due, as sometimes is erroneously supposed, to the resistance of the air to the passage of the bullet along the barrel, for even if the air were abolished, the recoil, so far as due to the masses and velocities, would remain the same, as indeed may be seen from the fact of our calculation taking no account of the bore of the rifle or of the shape of the bullet, circumstances of the utmost importance where atmospheric resistance is concerned.

The foregoing calculation however involves an assumption not in exact conformity with actual conditions, by taking for granted that the _centre of gravity_ of the rifle is in the line of the axis of the barrel, while in fact this centre is almost always lower, and therefore the kick of the recoil acts in part as a turning-over push, tending to tilt up the muzzle of the gun, and for that reason the firer must hold the weapon very firmly or he will miss his aim. When such a rifle as we have supposed is fired, say from the shoulder, it would follow from the above calculation that the backward kick of the recoil is equivalent to a blow from a 10–lb. weight moving at the speed of 7½ ft. per second. This would certainly be a very uncomfortable experience, but the backward momentum must be met somehow. We have supposed that the gun is free to move, but we know the firer presses it firmly against the muscles of his shoulder, and the stock of the gun is spread out and provided with a smooth hollow heel plate, so that any pressure from it is felt as little as possible, especially as the muscle against which it is applied acts as an elastic pad. With the rifle thus firmly held we may regard the marksman and his rifle as forming only _one mass_, and the centre of gravity of this being now much below the axis of the barrel, the effect of the recoil tends to overthrow the man backwards; but he learns to resist this by standing firmly, so that the elasticity of his whole frame comes into play; and besides this, the mass factor of the momentum being now so large, the velocity factor becomes comparatively insignificant.

Although the momenta of gun and projectile are, according to Newton’s law, _equal_ and opposite, the case is very different with regard to their _energies_, or powers of doing work, for the measure of these is jointly mass and _the square of the velocity_. The _energy_ (_vis viva_) of a body of weight in pounds = W, moving with the velocity of v feet per second is always Wv^2/64·4, that is, it will do this number of foot-lbs. units of work before it comes to rest. It would require too much space to demonstrate and fully explain here what this means, but the reader may refer to our index under the entries “Energy” and “Work,” or to any modern elementary treatise on dynamics. If the calculation be made of the energies of the ball and of the rifle due to our calculated velocities of recoil, it will be found that that of the ball is 160 times greater than that of the other, and the ball possesses this energy in a much smaller compass.

The course or track of a projectile through the air after it leaves the gun is called the _trajectory_, and this has been studied both experimentally and theoretically, with interesting results. Assuming that the shot passed through empty space, or that the air offered no resistance to its passage, it would be very easy to trace the path of a projectile. Let us suppose that Fig. 80 represents a gun elevated at a high angle. The moment the projectile leaves the muzzle, gravity begins to act upon it, causing it to move vertically downwards with ever-increasing velocity until it finally reaches the ground; the onward uniform movement parallel to the axis of the piece being continued all the time. We could find the position of the projectile at the end of successive equal periods of time by drawing a straight line AC, a prolongation of the axis of the piece, or a line of the same inclination; on this we mark off equal distances representing by scale the velocity of the projectile per second, the points B, C, D, E being the positions the projectile would be in at the end of each successive second if gravity did not act. In order to bring the diagram within moderate compass, we suppose the projectile to have only the small velocity of 115 ft. per second. At the end of the first second it would be at B, but now suppose that gravity is allowed to act for one second, it would at the end of that time have fallen 16 ft. vertically below B and have arrived at _b_. Similarly we may set off by scale on verticals through C, D, and E distances representing 64 ft., 144 ft., and 256 ft. respectively. Because, for instance, the ball, without gravity acting, would at the end of 3 seconds be at D, where we may suppose its course arrested and gravity then allowed to act for 3 seconds to pull the ball down from its position of rest at D; at the end of this period, gravity alone acting, its position would be 144 ft. vertically below D, because gravity pulls a body that distance in 3 seconds, and the actual position 3 seconds after the ball had left the muzzle would be at _d_, after it had described the curved path A, _b_, _c_, _d_. Supposing _d_ to be the highest point of the trajectory, another 3 seconds would bring the ball along a downward curve, and at the end of 6 seconds from the discharge it would be at a point on the same level as A. Now the complete curve would be symmetrical on each side of a vertical line through its highest point, and it would be in fact a regular _parabola_ with its vertex at _d_.

The foregoing presupposes that the air offers no resistance to the passage of the projectile through it. The fact however is quite otherwise, for no sooner does the projectile begin its flight than its velocity is constantly diminished by the air’s resistance. Now this resistance is complex, depending upon a number of different conditions, the effect of which can be taken into account only by extremely complex calculations. Obviously it will vary according to the area of the section presented by the projectile to the line of its flight, and again by the shape of its front, for a pointed shot will cleave the air with less resistance than one with a flat front. Then the density of the air at the time will also enter into the calculation. The mass of the projectile and also its velocity, upon which depend its _vis viva_, energy, or power of overcoming resistance in doing work, will also have to be considered. Most complex of all is the law, or rather laws (_i.e._ relations), which connect the air resistance with the velocity; for this relation no definite expression has been found. It is a function of the velocity (known only by experiment under defined conditions), and varying with the velocity itself. Thus for velocities up to 790 ft. per second, it is a function (determined experimentally) of the second power or square of the velocity; between 790 ft. per second and 990 ft. per second the law of resistance is changed and becomes a function of the third power of the velocity; between 990 ft. and 1,120 ft. velocity the law again changes and is related to the sixth power of the velocity; between 1,120 ft. and 1,330 ft. the resistance is again related to the third power of the velocity; and with higher speeds than that last named it is again more nearly related to the square of the velocity. It will be seen that to calculate the path of a projectile is really a very difficult mathematical problem, and indeed one which can be solved only approximately when all the known data are supplied.

The air resistance to the motion of a projectile is much greater than before trial would be supposed. Let us take an experiment that has actually been recorded, in which a bullet three-quarters of an inch in diameter, weighing one-twelfth of a pound, was found to have a velocity of 1,670 ft. per second at a distance of 25 ft. from the gun, and this 50 ft. farther was reduced to 1,550 ft. per second. Now if the reader will calculate, according to the formula we have given above, the _energy_ due to the bullet’s velocity at these points, he will find it must have done 500 foot-lbs. units of work in traversing the 50 ft., and as this could have been expended only in overcoming the resistance of the air, we learn that this last must have been equivalent to a mean or average pressure of 10 lbs. thrusting the bullet backwards.

It will be interesting to compare the difference in the trajectory of a projectile under defined conditions, worked out with the air resistance taken into account, compared with the trajectory when the air is supposed to be non-existent. We find an example of the former problem fully worked out by many elaborate mathematical formulæ in Messrs. Lloyd and Hadcock’s treatise on Artillery. The problem is thus stated:—“An 11–in. breech-loading howitzer” (a howitzer is a piece of ordnance used for firing at high angles) “fires a 600–lb. projectile with an initial velocity of 1,120 foot-sec. at an elevation of 20°. Find the range, time of flight, and angle of descent.” We shall calculate these points on the suppositions adopted with regard to Fig. 80, and with no higher mathematics than common multiplication and division.

It will have been observed that we supposed two motions that really take place simultaneously to take place successively and independently: one in the direction of the line of fire, due to the initial velocity; the other vertically downwards, due to the action of gravity, the final result being the same. This affords an excellent illustration of another of Newton’s laws of motion, and should be considered by the reader in this connection. The law itself admits of being stated in various ways, as thus:—“Whenever a force acts on a body, it produces upon it exactly the same change of motion in its own direction, whether the body be originally at rest or in motion in any direction with any velocity whatever—whether it be at the same time acted on by other forces or not.” Or again: “When two forces act in any direction whatever on a body free to move, they impress upon it a motion which is the _superposition_ (or compounding) of those that it would receive if each force acted separately.” The law is given also in the following form (Thomson and Tait):—“When any forces act on a body, then, whether the body be originally at rest or moving with any velocity and in any direction, each force produces in the body the exact change of motion which it would have had had it acted singly on the body originally at rest.” In all of these expressions the word “forces” is used, and a very convenient word it is, but it may be noted in passing, nothing but a word; for it stands for no real self-existing things, since, apart from observed changes of motion in bodies, forces for us have no existence. Nevertheless, it is useful for the sake of abbreviating statements about changes of motion, to regard these actions as produced by imaginary agents—imagined for the time and for this purpose, and therefore vainly to be sought for in the realm of reality.

In dealing with the trajectory of the howitzer’s projectile through airless space we have no concern with its diameter nor with its weight. We use the little diagram, Fig. 81, to represent the motions,—_c_ being a horizontal line, _a_, a vertical one, the angle at B is therefore a right angle, and we assume that at A to be 20°. Now, the most elementary geometry teaches us that every triangle having these angles will have the lengths of its sides in the same invariable proportions one to another whatever may be the size of the triangle itself, and it has been found convenient to calculate these proportions once for all, not merely for angle 20°, but for every angle up to 90°. Besides this, distinct names have been given to the proportions of every side of the triangle to each of the other two sides. Thus in the triangle before us, if we take _a_, _b_, and _c_ to represent the numbers expressing the lengths of the sides against which they are placed, _a_ divided by _b_, that is _a_ ÷ _b_, or _a_/_b_, is called the _sine_ of angle 20°, while _c_/_b_ is named the _cosine_ of that angle, etc. These therefore are _numbers_ which are given in mathematical tables, and we find by these that _sine_ 20° = 0·3420201, and _cosine_ 20° = 0·9396926, and these with the initial velocity give us all the data we require. We may first find the _time_ the projectile would take to reach the ground level, or strictly that of the muzzle of the gun at B. Taking _t_ to stand for this time, we know that AC = 1,120 × _t_, but CB will be the distance that a body would fall from rest at C by the influence of gravity in that same time, _t_, and it is known by experiment that this distance is 16·1 feet multiplied by the _square_ of the time from rest in seconds. We have now therefore the length of the line CB, and put _a_/_b_ = CB/AC = (16·1 × _t_^2)/(1,120 × _t_) = _sine_ 20° = ·3420201, and dividing numerator and denominator by _t_ and multiplying the above 3rd and 5th expressions by 1,120, we have

16·1 × _t_ = 1,120 × ·3420201

1,120 × ·3420201 and therefore _t_ = ———————————————— = 23·7927 secs. 16·1