Chapter VIII: Part 8

ON THE TIME TAKEN TO DRAW A BALL TO THE GROUND BY THE FORCE OF GRAVITY.

~If fired with axis parallel to the ground.~

1st Case. Supposing a ball to be fired when the axis of the piece is parallel to the ground and 16 feet above it, then the projectile will strike the earth in the same length of time that it would have done, had it been rolled out of the muzzle, quite irrespective of the velocity with which it may have been propelled, or the consequent extent of range; that is to say the ball will have reached the point B., (plate 22, fig. 1.), in the same length of time that it would require to fall from the muzzle A., to the earth C.; _i. e._, in one second.

2nd Case. Were three guns to be fired at the same instant, with their three axes parallel to the horizon as before, and loaded respectively with ¹⁄₂ drm., 1 drm., and 1¹⁄₂ drm. of powder of the same strength, then, although the three initial velocities and three ranges would consequently all be different, yet the three balls would strike the ground at the same time, _i. e._ at the points B. B. B. in one second. (Plate 22, fig. 2.)

~If axis at an angle to the ground.~

3rd Case. When a ball is fired at an angle of elevation it will reach the earth in the same length of time which it would occupy in falling the length of the tangent of the angle of projection; hence supposing F. G. (plate 22, fig. 3.) to be 16 feet, the ball would reach the point G. in one second, irrespective of the distance from D. to G.

ATMOSPHERE.

Let us now take into our consideration the course of a projectile while under the influence of _three_ forces, viz., powder, gravity, and air.

~Why named.~

The atmosphere, or sphere of gases, is the general name applied to the whole gaseous portion of this planet, as the term ocean is applied to its liquid, and land to its solid portions.

Being much lighter than either land or water, it necessarily floats or rests upon them, and is in sufficient quantity to cover the highest mountains, and to rise nine or ten times their height, to about 45 miles above the sea level, so as to form a layer over the whole surface, averaging probably between forty and fifty miles in thickness, which is about as thick, in proportion to the globe, as the liquid layer adhering to the surface of an orange, after it had been dipped in water.

~Composition of air.~

It consists essentially of two gases, called oxygen and nitrogen, and also contains a variable quantity of aqueous vapour.

~Qualities of air.~

In common with matter in every state, the air possesses impenetrability. It can be compressed, but cannot be annihilated. It has weight, inertia, momentum, and elasticity.

In consequence of its weight is its pressure, which acts uniformly on all bodies, and is equal to between 14lbs. and 15lbs. on every square inch of surface at the sea-level.

~Early idea of air’s resistance.~

~How air acts.~

The first experiments that were made on projectiles, were carried out on the idea that the resistance of the air would not materially affect the track of a bullet which had great velocity. But the moment a body is launched into space, it meets with particles of the air at every instant of its movement, to which it yields part of its velocity, and the air being a constant force, the velocity of the body decreases at every instant from the commencement of its motion.

RESULT OF THE AIR’S RESISTANCE.

~Robins, 1742, showed effect of air’s resistance.~

~Course of ball was not a parabola.~

~Why not a parabola.~

It remained for Robins, 1742, in a work then published, to show the real effect of the atmosphere upon moving bodies. He proved by actual experiment, that a 24lb. shot did not range the fifth part of the distance it should have done according to the parabolic theory. If a cannon shot moved in a parabolic curve, then from the known properties of that curve, it was evident that when fired with elevation, the angle of descent of the bullet should have been the same as the angle at which it was projected, and this he showed was not the case in practice. Now Robins acknowledged the opinion of Galileo, as regards the force of gravity, to be correct; he could not therefore attribute to him any miscalculation on the score of gravity. He therefore concluded, that the error of the “parabolic theory” arose from the supposition that the bullet continued to move at the same velocity throughout its course.

~Ballistic pendulum.~

Robins tried a series of experiments by firing at a ballistic pendulum at different distances; the oscillation of this pendulum enabled him to calculate the velocity of the bullet, at the time it struck the pendulum, and by this means he ascertained, that according to his expectations, the bullet moved slower in proportion as it became more distant from the point at which it was fired. This diminution he attributed to the resistance of the air.

~Trajectory more curved than a parabola.~

From these considerations it is evident that instead of moving over equal spaces A. C., C. D., D. E., (plate 22, fig. 4), at each succeeding second of time, it will require considerably longer to traverse each succeeding distance, and the force of gravity will consequently have longer time to act upon it, and will have the effect of lowering the bullet much more than it would do according to the “parabolic theory;” moreover it is evident, that as the velocity of the bullet diminishes, the trajectory or path followed by the bullet, will become still more incurvated.

Having now proved the error of the “parabolic theory,” Robins began his endeavours to calculate the actual course of the bullet, according to this new theory which he had demonstrated, but this calculation was necessarily attended with great difficulties, for in so doing a number of circumstances had to be considered.

~Resultant.~

The resultant of the three forces acting on a projectile, (plate 23, fig. 1), viz., gunpowder, gravity, and the resistance of the air, is a motal force, diminishing in velocity at every instant, causing the projectile to describe a curved line in its flight, the incipient point of the curve lying in the axis of the bore of the piece, and its continuation diverging in the direction of the attraction of gravity, till the projectile obeys the latter force alone.

EXPERIMENTS IN FRANCE.

~Angle for greatest range.~

~Velocity.~

It is stated by Captain Jervis, R.A., in the “Rifle Musket,” that “From experiments made in France, it has been found that the greatest range of the common percussion musket, with spherical bullet fired with the regulation charge, was at 25°; yet, by theoretical calculation, it should be 45°; also that the usual velocity was some 500 yards per second, whilst in vacuum it would be 19,792 yards per second.

~Elevation giving certain range.~

“At an angle of from 4° to 5°, the real range was about 640 yards; without the resistance of the air, and at an angle of 4¹⁄₂°, it would be 3,674, or six times greater.”

ON THE EFFECT OF THE RESISTANCE OF THE AIR UPON THE MOTION OF A PROJECTILE.

~The effect of the air’s resistance upon the motion of a projectile.~

The effect of the resistance of the atmosphere to the motion of a projectile, is a subject of the greatest importance in gunnery. It has engaged the attention of the most eminent philosophers, and on account of the great difficulty of determining by experiment, the correctness of any particular hypothesis, much difference of opinion is entertained as to the absolute effect of this retarding force upon bodies moving in the atmosphere with great velocities; and although sufficient is known to guide the practical artillerist in that art to which he is devoted, still as a scientific question, it is one of considerable interest, but more on account of the difficulty of its solution, than from its practical importance.

~Mr. Robins’ discoveries.~

To our distinguished countryman, Mr. Benjamin Robins, is due the credit of not only being the first practically to determine the enormous effect of the resistance of the air in retarding the motions of military projectiles, but also of pointing out and experimentally proving other facts with regard to this resistance, which will be noticed when considering the subject of the deviation of shot from the intended direction.

~Result of Dr. Hutton’s experiments.~

After him, Dr. Hutton made a great number of experiments upon the same point, viz., the effect of the resistance of the air upon bodies moving in that medium, both with great and small velocities; and the inferences which he drew from these experiments, although not absolutely true, are sufficiently correct for all practical purposes.

ON THE RESISTANCE OF A FLUID TO A BODY IN MOTION.

~Circumstances affecting the resistance which a body meets with in its
motion in a fluid.~

The resistance which a body meets with in its motion through a fluid will depend upon three principal causes, viz:--

1st. Its velocity, and the form and magnitude of the surface opposed to the fluid.

2nd. Upon the density and tenacity of the fluid or cohesion of its particles, and also upon the friction which will be caused by the roughness of the surface of the body.

3rd. Upon the degree of compression to which this fluid, supposed to be perfectly elastic, is subjected, upon which will depend the rapidity with which it will close in and fill the space behind the body in motion.

~The resistance of a fluid to a body as the squares of the
velocities.~

Firstly, with regard to the velocity of the body. It is evident that a plane moving through a fluid in a direction perpendicular to its surface, must impart to the particles of the fluid with which it comes in contact, a velocity equal to its own; and, consequently, from this cause alone, the resistances would be as the velocities; but the number of particles struck in a certain time being also as the velocities, from these two causes combined, the resistance of a fluid to a body in motion, arising from the inertia of the particles of the fluid, will be as the square of the velocity.

~Cohesion of the particles of a fluid, and friction.~

Secondly, a body moving in a fluid must overcome the force of cohesion of those parts which are separated, and the friction, both which are independent of the velocity. The total resistance then, from cohesion, friction, and inertia, will be partly constant and partly as the square of the velocity.

~Result.~

The resistances therefore are as the squares of the velocities in the same fluid, and as the squares of the velocities multiplied by the densities in different fluids.

Hitherto, however, we have imagined a fluid which does not exist in nature; that is to say, a _discontinued_ fluid, or one which has its particles separated and _unconnected_, and also perfectly non-elastic.

~Atmosphere, and its properties bearing on the question of its
resistance.~

Now, in the atmosphere, no one particle that is contiguous to the body can be moved without moving a great number of others, some of which will be distant from it. If the fluid be much compressed, and the velocity of the moving body much less than that with which the particles of the fluid will rush into vacuum in consequence of the compression, it is clear that the space left by the moving body will be almost instantaneously filled up, (plate 23, fig. 2); and the resistance of such a medium would be less the greater the compression, provided the density were the same, because the velocity of rushing into a vacuum will be greater the greater the compression. Also, in a greatly compressed fluid, the form of the fore part of the body influences the amount of the retarding force but very slightly, while in a non-compressed fluid this force would be considerably affected by the peculiar shape which might be given to the projectile.

~Resistance increased when the body moves so fast that a vacuum is
formed behind it.~

Thirdly. If the body can be moved so rapidly that the fluid cannot instantaneously press in behind it, as is found to be the case in the atmosphere, the resisting power of the medium must be considerably increased, for the projectile being deprived of the pressure of the fluid on its hind part, must support on its fore part the whole weight of a column of the fluid, over and above the force employed in moving the portion of the fluid in contact with it, which force is the sole source of resistance in the discontinued fluid. Also, the condensation of the air in front of the body will influence considerably the relation between the resistances and the velocities of an oblique surface: and it is highly probable that although the resistances to a globe may for slow motions be nearly proportional to the squares of the velocities, they will for great velocities increase in a much higher ratio.

ON THE VELOCITY WITH WHICH AIR WILL RUSH INTO A VACUUM.

~The velocity of the rush of air into a vacuum.~

When considering the resistance of the air to a body in motion, it is important that the velocity with which air will rush into a vacuum should be determined; and this will depend upon its pressure or elasticity.

~Result.~

It has been calculated, that air will rush into a vacuum at the rate of about 1,344 feet per second when the barometer stands at 30 inches, so that should a projectile be moving through the atmosphere at a greater velocity than this, say 1,600 feet per second, then would there be a vacuum formed behind the ball, and instead of having merely the resistance due to the inertia of the particles of the air, it would, in addition, suffer that from the whole pressure of a column of the medium, equal to that indicated by the barometer.

UPON THE RESISTANCE OF THE AIR TO BODIES OF DIFFERENT FORMS.

~Difficulties of the question.~

The influence of the form of a body upon the resistance offered to it by a fluid, is a problem of the greatest difficulty; and although the most celebrated mathematicians have turned their attention to the subject, still, even for slow motions, they have only been able to frame strictly empirical formula, founded upon the data derived from practice; while with regard to the resistance at very high velocities, such as we have to deal with, very little light has hitherto been thrown upon the subject.

~Compressed fluid.~

When a body moves in the atmosphere, the particles which are set in motion by the projectile, act upon those in proximity to them, and these again upon others; and also from the elasticity of the fluid, it would be compressed before the body in a degree dependant upon the motion and form of the body. Moreover, the atmosphere itself partakes so much of the nature of an infinitely compressed fluid, as to constantly follow the body without loss of density when the motion is slow, but not when the velocity is great, so that the same law will not hold good for both. In an infinitely compressed fluid (that is, one which would fill up the space left behind the body instantaneously) the parts of the fluid which the body presses against in its motion would instantaneously communicate the pressure received by them throughout the whole mass, so that the density of the fluid would not undergo any change, either in front of the body or behind it, consequently the resistance to the body would be much less than in a fluid partially compressed like the atmosphere; and the form of the body would not have the same effect in diminishing or increasing the amount of resistance.

~When a vacuum is formed behind the ball.~

When the velocity of a body moving in the atmosphere is so great that a vacuum is formed behind it, the action of the fluid approaches to that of the discontinued fluid.

RESULTS OF EXPERIMENTS WITH SLOW MOTIONS.

~Resistance in proportion to surface.~

1st. It appears from the various experiments that have been made upon bodies moving in the atmosphere, that the resistance is nearly as the surface, increasing a very little above that proportion in the greater surfaces.

~Resistance as squares of velocity.~

2nd. That the resistance to the same surface with _different_ velocities, is in _slow_ motions nearly as the squares of the velocity, but gradually increasing more and more in proportion as the velocities increase.

~Rounded and pointed ends suffer less resistance.~

3rd. The round ends, and sharp ends of solids, suffer less resistance than the flat or plane ends of the same diameter. Hence the flat end of the cylinder and of a hemisphere, or of a cone, suffer more resistance than the round or sharp ends of the same.

~Sharp ends not always least resistance.~

4th. The sharper ends have not always the smaller resistances; for instance, the round end of a hemisphere has less resistance than the pointed end of a cone, whose angle with the axis is 25° 42′.

~Form of base affects resistance.~

5th. When the hinder parts of bodies are of different forms, the resistances are different, though the fore parts are the same. Hence the resistance to the fore part of a cylinder is less than that on the equally flat surface of the cone or hemisphere, owing to the shape of the _base_ of the cylinder. The base of the hemisphere has less resistance than the cone, and the round side of the hemisphere less than that of the whole sphere.

~Only proved for slow motions.~

The above refers only to _slow_ motions, and the results given, from experiments with very small velocities; and it is to be expected, that with very rapid motions the form of the fore, as well as the hind part, of the projectile, will influence the amount of resistance in a much higher degree.

~Form of hind part.~

That form for the hind part will be best which has the greatest pressure upon it, when moving with a certain velocity.

~Best shape for fore and hind part.~

The ogivale form seems, from experiment, to fulfil the former condition. The best form for the _hind_ part, for _rapid_ motions, has not been determined; it may, however, be considered to be of much less importance than the shape of the fore part.

~Form determined by extent of range.~

Of course the best form can be determined by extent of range, but deductions from this will depend upon such a variety of circumstances, the effects of some of which must be entirely hypothetical, that the correctness of any formulæ obtained in this manner must be very uncertain.

~Form suggested by Sir I. Newton.~

Sir Isaac Newton, in his “Principia,” has given an indication of that form of body, which, in passing through a fluid, would experience less resistance than a solid body of equal magnitude of any other form. It is elongated.

~Axis of elongated bodies must be fixed.~

It is plain, however, that the minimum of resistance would not be obtained with a shot of an elongated form, unless the axis can be kept in the direction of the trajectory; as not only will the axis perpetually deviate from the true direction, but the projectile will turn over and rotate round its shorter axis, that is, if fired out of a smooth bore.

~Advantages of conical bullets.~

Conical bullets have an advantage, from their pointed end, which enables them to pass through the air with greater facility; and for the same reason they are better calculated to penetrate into any matter than spherical ones.

~Disadvantages of conical bullets.~

A _solid_ bullet cannot be pointed without sending backward the centre of gravity. The sharper the point, the more it is liable to injury, and if the apex of the cone does not lie true, in the axis of the projectile, then such an imperfection of figure is calculated to cause greater deflections in the flight than any injury which a round surface is likely to sustain. In penetrating into solid bodies, it is also important that the centre of gravity should be near its work.

RESISTANCE OF THE AIR, AS AFFECTED BY THE WEIGHT OF PROJECTILES.

~Resistance overcome by weight.~

Bodies of similar volume and figure overcome the resistance of the air in proportion to their densities. The amount of the air’s resistance is in proportion to the magnitude of the surface.

~Contents of circles.~

The superficial contents of circles are as the _squares_ of their diameters. Hence if the ball A. (plate 23, fig. 3) be 2in. in diameter, and the ball B. 4in., the amount of resistance experienced would be as four to sixteen.

~Contents of spheres.~

The cubical contents, or weights of spheres, are in proportion to the _cubes_ of their diameters. Hence the power to overcome resistance in the balls A and B would be as _eight_ to _sixty-four_. Thus the power to overcome resistance increases in much greater proportion than the resistance elicited by increasing the surface.

~Advantages of elongated bullets.~

Suppose an elongated body to have the diameter of its cylindrical portion equal to that of the ball A., _i.e._, E.F. = C.D., (plate 23, fig. 4), and elongated so that its weight should be equal to that of the spherical shot B., it is evident that it would meet equal resistance from the air, to the ball A., having, at the same time, as much power to overcome resistance as the body B.

Elongated balls, by offering a larger surface to the sides of the barrel, are less liable to be affected by any imperfections in the bore; whereas the spherical ball, pressing only on its tangential point, will give to any little hollows, or undulations, wherever they occur.

~Balls cannot be expanded.~

~Elongated projectiles easily expanded.~

A spherical ball cannot be expanded into the grooves, unless there be very little windage, except by blows from the ramrod, the gas escaping round the circumference of the ball, and giving it an irregular motion while passing down the barrel; but an elongated projectile can be readily expanded, and the facility of doing so is in proportion to the difference of length between its major and minor axis.

DEVIATIONS OF PROJECTILES FROM SMOOTH-BORED GUNS.

~Causes of deviation of shot.~

Very great irregularities occur in the paths described by projectiles fired from smooth-bored guns. It is a fact well known to all practical artillerists, that if a number of solid shot or any other projectile be fired from the same gun, with equal charges and elevations, and with gunpowder of the same quality, the gun carriage resting on a platform, and the piece being laid with the greatest care before each round, very few of the shot will range to the same distance; and moreover, the greater part will be found to deflect considerably (unless the range be very short) to the right or left of the line in which the gun is pointed.

~Four causes of deviation.~

The causes of these deviations may be stated as follows:--1st, Windage; 2nd, Rotation; 3rd, Wind; 4th, from Rotation of the Earth.

1st CAUSE, WINDAGE.

~Action from windage.~

~False direction.~

~Gives rotation.~

Windage causes irregularity in the flight of a projectile, from the fact of the elastic gas acting in the first instance on its upper portion, and driving it against the bottom of the bore; the shot re-acts at the same time that it is impelled forward by the charge, and strikes the upper surface of the bore some distance down, and so on by a succession of rebounds, until it leaves the bore in an accidental direction, and with a rotatory motion, depending chiefly on the position of the last impact against the bore. Thus should the last impact of a (concentric) shot when fired from a gun be upon the right hand side of the bore, as represented, (plate 23, fig. 5); the shot will have a tendency to deflect to the left in the direction. While at the same time a rotation will be given to it in the direction indicated by the arrows.

2nd CAUSE, ROTATION.

~Rotation without translation.~

Every body may have a twofold motion, one by which it is carried forward, and the other by which it may turn round on an axis passing through its centre, called a motion of rotation.

When a body has only a motion of translation all the particles of which it is composed move with equal swiftness, and also in parallel directions; and by the first law of motion, every particle put in such motion will constantly move with the same velocity in the same direction, unless it be prevented by some external cause.

~Rotation.~

~Rotation and translation combined.~

By a motion of rotation, a body without changing its place, turns round on an axis passing through its centre of gravity. A body may have at the same time both a progressive and rotatory motion, without either disturbing the other, and one may suffer a change from the action of some external force, while the other continues the same as before.

~Force through centre of gravity, causes progressive motion only.~

If the direction of the force be through the centre of gravity, it causes a progressive motion only, that is, if the body was at rest before, it will move forward in the direction of the impressed force.

~Effect of force on a body in motion.~

If a body had a progressive motion before, then impressed force will cause it to move faster or slower, or to change its direction, according as the direction of this second force conspires with or opposes its former motion, or acts obliquely on its direction.

~Rotation not disturbed by second force in direction of centre of
gravity.~

If a body, besides its progressive motion had a motion of rotation also, this last will not be changed by the action of a new force passing through the centre of gravity.

~Rotation of force does not pass through the centre of gravity.~

If the direction of the force does not pass through the centre of gravity, the progressive motion will be altered, and the body will then also acquire a rotatory motion round an axis passing through the centre of gravity, and perpendicular to a plane passing through the direction of the force and this centre.

CASES BEARING UPON THE FOREGOING THEORY.

~When ball is perfectly round, centre of gravity coincides with
figure, and no windage.~

1st Case. Suppose the ball to be perfectly round, its centre of gravity and figure to coincide, and let there be no windage. In this case the force of the powder not only passes through the centre of gravity of the shot, but proceeds in a direction parallel to the axis of the bore, and there would be but small friction due to the weight of the shot.

~If windage then rotation.~

2nd Case. But as there is a considerable amount of friction between the bore and the projectile in the case where there is windage, the direction of this force being opposite to that of the gunpowder, and upon the surface of the ball, it will therefore give rotation to the shot.

~Eccentricity causes rotation.~

3rd Case. Suppose the ball to be perfectly round, but its centre of gravity not to coincide with the centre of figure. In this case the impelling force passes through the centre of the ball, or nearly so, and acts in a direction parallel to the axis of the piece; but if the centre of gravity of the ball lie out of the line of direction of the force of the powder, the shot will be urged to turn round its centre of gravity.

~Angular velocity.~

The angular velocity communicated to the body will depend, firstly, upon the length of the perpendicular from the centre of gravity upon the direction of the impelling force, and secondly, upon the law of density of the material or the manner in which the metal is distributed. The direction of rotations will depend upon the position of the centre of figure with regard to that of gravity. (Plate 23, fig. 6.)

~Robins’ remarks.~

Robins remarks, bullets are not only depressed beneath their original direction by the action of gravity, but are also frequently driven to the right or left of that direction by the action of some other force. If it were true that bullets varied their direction by the action of gravity only, then it ought to happen that the errors in their flight to the right or left of the mark, should increase in proportion to the distance of the mark from the firer only.

~Deflection not in proportion to distance.~

But this is contrary to all experience, for the same piece which will carry its bullet within an inch at ten yards, cannot be relied upon to ten inches in one hundred yards, much less to thirty inches in three hundred.

Now this irregularity can only arise from the track of the bullet being incurvated sideways as well as downwards. The reality of this doubly incurvated track being demonstrated, it may be asked what can be the cause of a motion so different from what has been hitherto supposed.

~1st cause of increase, deflection.~

1st Cause. Is owing to the resistance of the air acting obliquely to the progressive motion of the body, and sometimes arises from inequalities in the resisted surface.

~2nd cause, from whirling motion.~

~Direction of a shot influenced by position of axis round which it
whirls.~

2nd Cause. From a whirling motion acquired by the bullet round its axis, for by this motion of rotation, combined with the progressive motion, each part of the bullet’s surface will strike the air in a direction very different from what it would do if there was no such whirl; and the obliquity of the action of the air arising from this cause will be greater, according as the rotatory motion of the bullet is greater in proportion to its progressive motion; and as this whirl will in one part of the revolution conspire in some degree with the progressive, and in another part be equally opposed to it, the resistance of the air on the fore part of the bullet will be hereby affected, and will be increased in that part where the whirling motion conspires with the progressive; and diminished where it is opposed to it. And by this means the whole effort of resistance, instead of being in a direction opposite to the direction of the body, will become oblique thereto, and will produce those effects we have already mentioned. For instance, if the axis of the whirl was perpendicular to the horizon, then the incurvation would be to the right or left. If that axis were horizontal to the direction of the bullet, then the incurvation would be upwards or downwards. But as the first position of the axis is uncertain, and as it may perpetually shift in the course of the bullet’s flight, the deviation of the bullet is not necessarily either in one certain direction, nor tending to the same side in one part of its flight that it does in another, but it more usually is continually changing the tendency of its deflection, as the axis round which it whirls must frequently shift its position during the progressive motion.

~Doubly incurvated track.~

It is constantly found in practice that a shot will deviate in a curved line, either right or left, the curve rapidly increasing towards the end of the range. This most probably occurs from the velocity of rotation decreasing but slightly, compared with the initial velocity of the shot, or, if a strong wind is blowing across the range during the whole time of flight, the curve would manifestly be increased according as the velocity of the ball decreased.

ILLUSTRATIONS OF ROBINS’ THEORY OF ROTATION.

~With ball and double string.~

1st Illustration. A wooden ball 4¹⁄₂ inches in diameter suspended by a double string, nine feet long. It will be found that if this ball receive a spinning motion by the untwisting of the string it will remain stationary. If it be made to vibrate, it will continue to do so in the same vertical plane. But if it be made to spin while it vibrates it will be deflected to that side on which the whirl combines with the progressive motion.

~By firing through screens.~

2nd Illustration. By firing through screens of thin paper placed parallel to each other, at equal distances, the deflection or track of bullets can easily be investigated. It will be found that the amount of deflection is wholly disproportioned to the increased distance of the screens.

~Bent muzzle.~

3rd Illustration. To give further light upon this subject, Mr. Robins took a barrel and bent it at about three or four inches from the muzzle to the left, the bend making an angle of 3° or 4° with the axis of the piece.

By firing at screens it was found that although the ball passed through the first screens to the left, it struck the butt to the right of the vertical plane on which aim was taken in line of the axis of the unbent portion of the barrel. This was caused by the friction of the ball on the right side of the bent part of the muzzle, causing the ball to spin from left to right.

ON ECCENTRIC PROJECTILES.

~How to find centre of gravity.~

Sir Howard Douglas, in his “Naval Gunnery,” states:--“The position of the centre of gravity can be found by floating the projectile in mercury, and marking its vertex. Then mark a point upon the shot diametrically opposite to that point, which will give the direction of the axis in which the two centres lie. Thus the shot can be placed in the gun with its centre of gravity in any desired position.”

~Effect of eccentricity.~

“On making experiments, it appeared that not one shot in a hundred, when floated in mercury, was indifferent as to the position in which it was so floated, but turned immediately, until the centre of gravity arrived at the lowest point, and consequently that not one shot in a hundred was perfect in sphericity, and homogeneity. Shells can be made eccentric by being cast with a solid segment in the interior sphere, left in the shell, or by boring two holes in each shell, diametrically opposite to one another, stopping up one with 5lbs. of lead, and the other with wood. When the centre of gravity was above the centre of the figure, the ranges were the longest, and when below, the shortest. When to the right or left hand, the deviations were also to the right or left. The mean range which, with the usual shot, was 1640 yards, was, with the shot whose centres of gravity and of figure were not coincident, the centre of gravity being upwards, equal to 2140 yards, being an increase of 500 yards.

~Ricochet of eccentric shot.~

“With respect to the ricochet of eccentric spherical projectiles, the rotation which causes deflection in the flight, must act in the same manner to impede a straight forward graze. When an ordinary well formed homogenous spherical projectile, upon which probably very little rotation is impressed, makes a graze, the bottom of the vertical diameter first touches the plane, and immediately acquires, by the reaction, a rotation upon its horizontal axis, by which the shot rolls onwards throughout the graze, probably for a straight forward second flight. But in the case of an eccentric spherical projectile, placed with its centre of gravity to the right or to the left, its rotation upon its vertical axis during the graze must occasion a fresh deflection in its second flight, and it is only when the centre of gravity is placed in a vertical plane passing through the axis of the gun, that the rotation by touching the ground will not disturb the direction of the graze, though the extent of range to the first graze will be affected more or less according as the centre of gravity may have been placed upwards or downwards. Whether the rebounds take place from water, as in the experiments made on board the “Excellent,” or on land, as those carried on at Shoeburyness, the shot, when revolving on a vertical axis, instead of making a straight forward graze, suffered deflection which were invariably towards the same side of the line of fire as the centre of gravity; and at every graze up to the fourth, a new deflection took place.

~Knowledge derived from experiments with eccentric shot.~

“The results of these very curious and instructive experiments fully explain the extraordinary anomalies, as they have heretofore been considered, in length of range and in the lateral deviations: these have been attributed to changes in the state of the air, or the direction of the wind, to differences in the strength of the gunpowder, and to inequalities in the degrees of windage. All these causes are, no doubt, productive of errors in practice, but it is now clear that those errors are chiefly occasioned by the eccentricity and nonhomogeneity of the shot, and the accidental positions of the centre of gravity of the projectile with respect to the axis of the bore. The whole of these experiments furnish decisive proof of the necessity of paying the most scrupulous attention to the figure and homogeneity of solid shot, and concentricity of shells, and they exhibit the remarkable fact that a very considerable increase of range may be obtained without an increase in the charge, or elevation of the gun.”

~No advantage in using eccentric projectiles.~

It is not to be expected that eccentric projectiles would be applicable for general purposes, on account of the degree of attention and care required in their service, nor would much advantage be gained by their use, as the momentum is not altered, and it is only necessary to give the ordinary shot a little more elevation in order to strike the same object.

~Range of elongated projectiles at certain low elevations greater in
air than in vacuo.~

There is another point of great importance with regard to the range of elongated projectiles. It is asserted by Sir W. Armstrong and others, that at certain low elevations the range of an elongated projectile is greater in the atmosphere than in vacuo, and the following is the explanation given by the former of this apparent paradox. “In a vacuum, the trajectory would be the same, whether the projectile were elongated or spherical, so long as the angle of elevation, and the initial velocity were constant; but the presence of a resisting atmosphere makes this remarkable difference, that while it greatly shortens the range of the round shot, it actually prolongs that of the elongated projectile, provided the angle of elevation do not exceed a certain limit, which, in my experiments, I have found to be about 6°. This appears, at first, very paradoxical, but it may be easily explained. The elongated shot, if properly formed, and having a sufficient rotation, retains the same inclination to the horizontal plane throughout its flight, and consequently acquires a continually increasing obliquity to the curve of its flight. Now the effect of this obliquity is, that the projectile is in a measure sustained upon the air, just as a kite is supported by the current of air meeting the inclined surface, and the result is that its descent is retarded, so that it has time to reach to a greater distance.”

~Charge.~

The form and weight of the projectile being determined as well as the inclination of the grooves, the charge can be so arranged as to give the necessary initial velocity, and velocity of rotation; or if the nature of projectile and charge be fixed, the inclination of the grooves must be such as will give the required results. The most important consideration is the weight and form of projectile; the inclination of the grooves, the charge, weight of metal in the gun, &c., are regulated almost entirely by it. The charges used with rifle pieces are much less than those with which smooth-bored guns are fired, for little or none of the gas is allowed to escape by windage, there being therefore no loss of force; and it is found by experience that, with comparatively low initial velocities, the elongated projectiles maintain their velocity, and attain very long ranges.

NOTE.--The foregoing articles on “Theory,” are principally extracted
from “New Principles of Gunnery by Robins,” “Treatise on Artillery, by
Lieut.-Colonel Boxer, R.A.” “The Rifle Musket, by Captain Jervis,
M.P., Royal Artillery.” “Elementary Lecturers on Artillery, by Major
H. C. Owen and Captain T. Dames, Royal Artillery.”

THE END.

FIG. 1.

Powder Mill.

FIG. 2.

Old Eprouvette Pendulum

FIG. 3.

New Pattern Eprouvette

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

Hydraulic Press

_Enlarged section of Valve_

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

Robins’ Balistic Pendulum

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

Bow unstrung

FIG. 2.

Bow strung

FIG. 3.

Hand or Arrow Rocket

FIG. 4.

Five barrelled Matchlock

FIG. 5.

Revolving Barrelled Matchlock

CHINESE EXPLOSIVE AND OTHER WEAPONS.

FIG. 6.

Asiatic Bow

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen]

FIG. 1.

Matchlock

FIG. 2.

Breech loading Gingal (Chamber in)

FIG. 3.

Breech loading Gingal (Chamber out)

CHINESE EXPLOSIVE ARMS.

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

FIG. 4.

_Harry Vernon dele._

MACHINES FOR THROWING DARTS AND STONES.

Day & Son Lith^{rs}. to the Queen.]

ONAGER (SLUNG).

_Harry Vernon delt._

Day & Son, Lith^{rs}. to the Queen.]

Onager (unslung).

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

Balista

_Arthur Walker C.^{t} 79.^{th} delt._

Day & Son Lith^{rs}. to the Queen.]

Catapulta.

_Dessiné par Arthur Walker._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

Staff slings, Longbows, Crossbows and Flail.

FIG. 2.

Onager.

FIG. 3.

Trepied.

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

Detail of Springs.

Balista.

_Harry Vernon Staff Serj^{t}. del._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

_Harry Vernon delt._

A Cross bow man and Slinger.

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

FIG. 4.

Cross-bows and Quarrels.

_Harry Vernon delt._

Day & Son Lith^{rs}. to the Queen.]

_Harry Vernon delt._

A Cross bow man and his Paviser.

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

Gun and Querrel Temp: Edward 3^{rd}. Sloane M^{ss}.

FIG. 2.

Small chambered Cannon from the Santini M^{ss}.

FIG. 3.

Santini M^{ss}. Early part of 15^{th} Cent^{y}.

FIG. 4.

Mode of mounting from Froissart.

FIG. 5.

Method of obtaining elevation.

FIG. 6.

Mode of Mounting from Valturius.

FIG. 7.

From the wreck of the “Mary Rose” Temp: Henry 8^{th}.

FIG. 8.

Hooped Cannon in wooden bed.

FIG. 9.

Ancient Screw piece.

FIG. 10.

Ancient Screw Breech loader.

FIG. 11.

Chinese Field piece Peiho 1860.

FIG. 12.

Ancient howitzer Cannon for throwing balls Filled with powder

_Arthur Walker delt._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

Giorgio Martini, 15^{th}. Century, latter part.

FIG. 2.

Queen Elizabeth’s Pocket Pistol.

Mons Meg.

Chamber.

Pierrier or Paterera__16^{th}. Century.

_H. Cautly del._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

Cart of War.__Temp: Henry 8^{th}.

FIG. 2.

“Moolik i Meidan.”

FIG. 3.

Bombard and Carriage.__15^{th}. Cent^{y}.

FIG. 4.

Long Serpentine of Wrought Iron.__15^{th}. Cent^{y}.

_R.G. Coles del.^{t}_

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

FIG. 4.

FIG. 5.

FIG. 6.

FIG. 7.

FIG. 8.

FIG. 9.

Musketeer 16^{th}. Cent^{y}.

FIG. 10.

Earliest form of Hand Gun.

FIG. 11.

FIG. 12.

_Arthur Walker, delt._

Day & Son Lith^{rs}. to the Queen.]

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

FIG. 4.

FIG. 5.

_Arthur Walker del._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

FIG. 4.

_Arthur Walker L^{t}. 79^{th}. del._

Day & Son Lith^{rs}. to the Queen.]

FIG. 1.

FIG. 2.

FIG. 3.

FIG. 4.

FIG. 5.

FIG. 6.

_Harry Vernon Staff Serj^{t}. del._

Day & Son Lith^{rs}. to the Queen.]

Extended Table of Contents

Page
INTRODUCTION. i

CONTENTS iii

ERRATA. iv

HISTORY OF GUNPOWDER. 1
GREEK FIRE. 4

ON THE MANUFACTURE OF GUNPOWDER. 7
SALTPETRE, OR NITRE. 7
OLD METHOD. 7
NEW METHOD. 8
CHARCOAL. 9
SULPHUR. 11
PULVERIZING THE INGREDIENTS. 11
MIXING THE INGREDIENTS. 12
THE INCORPORATING MILL. 12
INCORPORATING THE INGREDIENTS. 13
BREAKING DOWN THE MILL CAKE. 14
PRESSING THE MEAL BY THE HYDRAULIC PRESS. 14
GRANULATING THE PRESS CAKE. 15
DUSTING LARGE-GRAIN POWDER. 16
DUSTING FINE-GRAIN POWDER. 17
GLAZING FINE-GRAIN POWDER. 17
STOVING OR DRYING POWDER. 17
FINISHING DUSTING. 17
EXAMINATION AND PROOF OF GUNPOWDER. 18
PROOF OF MERCHANT’S POWDER. 18
REMARKS ON THE PROOF OF POWDER BY THE EPROUVETTES. 19
OF THE SIZE OF GRAIN FOR GUNPOWDER. 19
OBSERVATIONS ON THE MANUFACTURE OF GUNPOWDER ON THE CONTINENT
AND AMERICA. 20
PRODUCTION AND PURIFICATION OF THE INGREDIENTS. 20
PULVERIZING AND MIXING THE INGREDIENTS. 20
INCORPORATING PROCESS. 21
GRANULATING. 21
STOVING OR DRYING. 21
NEW RIFLE POWDER. 22

ON MAGAZINES. 23

LIGHTNING CONDUCTORS. 24

ON THE EXPLOSIVE FORCE OF GUNPOWDER. 29
FOULING. 35
EFFECTS OF GUNPOWDER ON METALS. 35
MISCELLANEOUS EXPERIMENTS. 36
ON THE TIME REQUIRED FOR IGNITION OF GUNPOWDER. 38
EFFECTS OF ACCIDENTAL EXPLOSIONS OF GUNPOWDER. 38

ON ANCIENT ENGINES OF WAR. 39
THE SLING. 43
THE BOW. 44
MERITS OF THE LONG BOW. 45
Our Forefathers encouraged to acquire skill in archery by legal
enactments, and by the founders of our public schools. 47
1ST. BY LEGAL ENACTMENTS. 47
2ND.—BY THE FOUNDERS OF OUR PUBLIC SCHOOLS. 48
MEANS BY WHICH SKILL IN ARCHERY WAS ACQUIRED. 49
PROOFS OF THE IMPORTANCE OF ARCHERY. 52
MILITARY AND POLITICAL CONSEQUENCES OF SKILL IN THE USE OF THE
BOW. 53
THE ARBALEST, OR CROSS-BOW. 54
DESCRIPTION OF CROSS-BOW. 57
COMPARATIVE MERITS OF THE LONG AND CROSS BOW. 59
COMPARATIVE MERITS BETWEEN BOWS AND EARLY FIRE-ARMS. 59

HISTORY OF ARTILLERY. 62
ETYMOLOGIES. 72

HISTORY OF PORTABLE FIRE-ARMS. 73

THE BAYONET. 83

ACCOUTREMENTS AND AMMUNITION. 84

HISTORY OF THE RIFLE. 86
RIFLED BREECH-LOADERS. 92

ON RIFLING. 95
ON THE NUMBER, FORM &c., &c., &c., OF THE GROOVES. 96
ON RIFLE PROJECTILES. 101
CONCLUSION. 108

THEORETICAL PRINCIPLES. 110
DEFINITIONS. 110
MOTION OF A PROJECTILE. 111
GRAVITY. 113
ON THE TIME TAKEN TO DRAW A BALL TO THE GROUND BY THE FORCE OF
GRAVITY. 114
ATMOSPHERE. 115
RESULT OF THE AIR’S RESISTANCE. 115
EXPERIMENTS IN FRANCE. 116
ON THE EFFECT OF THE RESISTANCE OF THE AIR UPON THE MOTION OF
A PROJECTILE. 117
ON THE RESISTANCE OF A FLUID TO A BODY IN MOTION. 117
ON THE VELOCITY WITH WHICH AIR WILL RUSH INTO A VACUUM. 118

UPON THE RESISTANCE OF THE AIR TO BODIES OF DIFFERENT FORMS. 119
RESULTS OF EXPERIMENTS WITH SLOW MOTIONS. 119
RESISTANCE OF THE AIR, AS AFFECTED BY THE WEIGHT OF PROJECTILES. 121
DEVIATIONS OF PROJECTILES FROM SMOOTH-BORED GUNS. 121
1st CAUSE, WINDAGE. 121
2nd CAUSE, ROTATION. 122
CASES BEARING UPON THE FOREGOING THEORY. 122
ILLUSTRATIONS OF ROBINS’ THEORY OF ROTATION. 124
ON ECCENTRIC PROJECTILES. 124

Original Table of Contents

Transcriber’s Notes

The original language has been retained, including inconsistencies and
errors in spelling, hyphenation, capitalisation, etc., except as
mentioned below.

Depending on the hard- and software used and their settings, not all
elements may display as intended.

Table of Contents: as present in the source document. The reason for
the order of entries is not clear, and some chapters are not listed,
nor are the sections. The structure of the text has been determined
based on what seemed the most logical interpretation of (the lay-out
of) the chapter and section headings in the text. The Extended Table
of Contents in the back of the book has been created for this text on
the basis of this assumed structure.

The text refers to the plates by both Roman and Arabic numbers. This
has not been standardised. The numbering of the actual plates has been
standardised.

Page 29, great inconvenience ... quite preclude: as printed in the
source document.

Page 29 and 35 (and Errata), sulphite and sulphide: as printed in the
source document.

Page 30 and 31, calculations: as printed in the source document.

Page 44, Slings were used in 1572, at the siege of Sancere by the
Huguenots, in order to save their powder: there should be a comma
after Sancere, the Huguenots were the besieged party.

Page 47, Our forefathers ... public schools: considered to be a
section heading.

Page 66, both the king’s feed men: other sources mention Peter Bawd
and Peter Vancollen / Van Collen as freed men.

Page 107, weight of bullet, ·530 grains: as printed in the source
document, but unlikely to be correct.

Page 114, paragraph on Parabolic theory: even with the corrections
mentioned in the errata, some of the reference letters are missing; F,
G and H are presumably the ends of the vertical lines through C, D and
E respectively.

Page 119, strictly empirical formula: should probably have been a
plural.

Changes made:

Sidenotes have been moved to directly before, footnotes have been
moved to directly after the paragraph to which they refer.

Some minor obvious punctuation and typographical errors have been
corrected silently.

B.C./B. C. and A.D./A. D. have been standardised to B. C. and A. D.,
respectively. Minie, Miniè (the spelling used most commonly in this
book) and Minié have been standardised to Minié.

The (corrected, see below) Errata have already been applied to the
text.

Errata: Page 32, para. 6, line 10 changed to Page 32, para.7, line 10;
IX and XII changed to ix and xii; Page 84, para. 2, line 1 (2nd entry)
changed to Page 84, para. 3, line 1. Subalterns changed to subaltern
officers; Page 91, para. 5 changed to Page 91, para. 4; sign changed
to sine.

Page 4: Poganatus changed to Pogonatus as elsewhere

Page 5: Talavara changed to Talavera

Page 21: frustrum changed to frustum

Page 30: 3490 changed to 3940

Page 32, sidenote: Robert changed to Piobert (as in text and Errata)

Page 35: deliquescient changed to deliquescent

Page 38: dull read heat changed to dull red heat

Page 52: closing quote mark inserted after Shooting-fields

Page 54: yeoman or archers changed to yeomen or archers

Page 61: opening quote mark inserted before Report of the Rifle Match

Page 65: opening quote marks inserted before Musée

Page 74, sidenote: 1491 changed to 1471

Page 86, Bàle changed to Bâle

Page 88, sidenote: Carabine a Tige changed to Carabine à Tige

Page 105: cups divers shapes changed to cups of divers shapes

Page 115: Plate 21, fig. 2 changed to Plate 22, fig. 2

Plate 18: opening quote marks inserted before Moolik.