GUNNERY
, the art of charging, directing, and exploding fire-arms, as cannon, mortars, muskets, &c, to the best advantage.
Gunnery is sometimes considered as a part of the military art, and sometimes as a part of pyrotechny. To the art of Gunnery too belongs the knowledge of the force and effect of gunpowder, the dimensions of the pieces, and the proportions of the powder and ball they carry, with the methods of managing, charging, pointing, spunging, &c. Also some parts of Gunnery are brought under mathematical consideration, which among mathematicians are called absolutely by the name Gunnery, viz, the rules and method of computing the range, elevation, quantity of powder, &c, so as to hit a mark or object proposed, and is more particularly called Projectiles; which see.
History of Gunnery.
Long before the invention of gunpowder, and of Gunnery, properly so called, the art of artillery, or projectiles, was actually in practice. For, not to mention the use of spears, javelins, or stones thrown with the hand, or of bows and arrows, all which are found among the most barbarous and ignorant people, ac- counts of the larger machines for throwing stones, darts, &c, are recorded by the most ancient writers. Thus, one of the kings of Judah, 800 years before the christian æra, erected engines of war on the towers and bulwarks of Jerusalem, for shooting arrows and great stones for the defence of that city. 2 Chron. xxvi. 15. Such machines were afterwards known among the Greeks and Romans by the names of Ballista, Catapulta, &c, which produced effects by the action of a spring of a strongly twisted cordage, formed of tough and elastic animal substances, no less terrible than the artillery of the moderns. Such warlike instruments continued in use down to the 12th and 13th centuries, and the use of bows still longer; nor is it probable that they were totally laid aside till they were superseded by gunpowder and the modern ordnance.
The first application of gunpowder to military affairs, it seems, was made soon after the year 1300, for which the proposal of friar Bacon, about the year 1280, for applying its enormous explosion to the destruction of armies, might give the first hint; and Schwartz, to whom the invention of gunpowder has been erroneously ascribed, on account of the accident abovementioned under the article Gun, might have been the first who actually applied it in this way, that is in Europe; for as to Asia, it is probable that the Chinese and Indians had something of the kind many ages before. Thus, only to mention the prohibition of fire-arms in the co<*>e of Gentoo laws, printed by the East India Company in 1776, which seems to confirm the suspicion suggested by a passage in Quintus Curtius, that Alexander the Great found some weapons of that kind in India: Cannon in the Shansorit idiom is called shet-aghnee, or the weapon that kills a hundred men at once.
However, the first pieces of artillery, which were charged with gunpowder and stone bullets of a prodigious size, were of very clumsy and inconvenient structure and weight. Thus, when Mahomet the 2d besieged Constantinople in 1453, he battered the walls with stones of this kind, and with pieces of the calibre of 1200 pounds; which could not be fired more than four times a day. It was however soon discovered that iron bullets, of much less weight than stone ones, would be more efficacious if impelled by greater quantities of stronger powder. This occasioned an alteration in the matter and form of the cannon, which were now cast of brass. These were lighter and more manageable than the former, at the same time that they were stronger in proportion to their bore. This change took place about the close of the 15th century.
By this means came first into use such powder as is now employed over all Europe, by varying the proportion of the materials. But this change of the proportion was not the only improvement it received. The practice of graining it is doubtless of considerable advantage. At first the powder had been always used in the form of fine meal, such as it was reduced to by grinding the materials together. And it is doubtful whether the first graining of powder was intended to increase its strength, or only to render it more convenient for filling into small charges and the charging of small arms, to which alone it was applied for many years, whilst meal-powder was still used for cannon.| But at last the additional strength which the grained powder was found to possess, doubtless from the free passage of the air between the grains, occasioned the meal-powder to be entirely laid aside.
For the last 200 years, the formation of cannon has been very little improved; the best pieces of modern artillery differing little in their proportions from those used in the time of Charles the 5th. Indeed lighter and shorter pieces have been often proposed and tried; but though they have their advantages in particular cases, it is agreed they are not sufficient for general service. Yet the size of the pieces has been much decreased; the same purposes being now accomplished, by smaller pieces than what were formerly thought necessary. Thus the battering cannon now approved, are those that formerly were called demi cannon, carrying a ball of 24 pounds weight; this weight having been sound fully sufficient. The method also of making a breach, by first cutting off the whole wall as low as possible before its upper part is attempted to be beaten down, seems to be a considerable modern improvement in the practical part of gunnery. But the most considerable improvement in the practice, is the method of firing with small quantities of powder, and elevating the piece but a little, so that the bullet may just go clear of the parapet of the enemy, and drop into their works, called ricochet firing: for by this means the ball, coming to the ground at a small angle, and with a small velocity, does not bury itself, but bounds or rolls along a great way, destroying all before it. This method was first practised by M. Vauban at the siege of Aeth, in the year 1692. A practice of this kind was successfully used by the king of Prussia at the battle of Rosbach in 1757. He had several six-inch mortars, made with trunnions, and mounted on travelling carriages, which were fired obliquely on the enemy's lines, and among their horse. These being charged with only 8 ounces of powder, and elevated at one degree and a quarter, did great execution: for the shells rolling along the lines with burning fuses made the stoutest of the enemy not wait for their bursting.
The use of fire-arms was however long known before any theory of projectiles was formed. The Italians were the first people that made any attempts at the theory, which they did about the beginning of the 16th century, and amongst them it seems the first who wrote professedly on the flight of cannon shot, was Nicholas Tartalia, of Brescia, the same author who had so great a share in the invention of the rules for cubic equations. In 1537 he published, at Venice, his Nova Scientia, and in 1546 his Quesiti & Inventioni diversi, in both which he treats professedly on these motions, as well as in another work, translated into English with additions by Cyprian Lucar, under the title of Colloquies concerning the Art of Shooting in great and small Pieces of Artillery, and published at London in 1588. He determined, that the greatest range of a shot was when discharged at an elevation of 45°: and he asserted, contrary to the opinion of his contemporaries, that no part of the path described by a ball is a right line; although the curvature in the first part of it is so small, that it need not be attended to. He compared it to the surface of the sea; which, though it appears to be a plane, is yet doubtless incurvated round the centre of the earth. He says he invented the gunner's quadran<*> for laying a piece of ordnance at any point or degree of elevation; and though he had but little opportunity of acquiring any practical knowledge by experiments, he yet gave shrewd guesses at the event of some untried methods.
The philosophers of those times also took part in the questions arising upon this subject; and many disputes on motion were held, especially in Italy, which continued till the time of Galileo, and probably gave rise to his celebrated Dialogues on Motion. These were not published till the year 1638; and in the interval there were published many theories of the motion of military projectiles, as well as many tables of their comparative ranges; though for the most part very fallacious, and inconsistent with the motions of these bodies.
It is remarkable however that, during these contests, so few of those who were intrusted with the care of artillery, thought it worth while to bring their theories to the test of experiment. Mr. Robins informs us, in the preface to his New Principles of Gunnery, that he had met with no more than four authors who had treated experimentally on this subject. The first of these is Collado, in 1642, who has given the ranges of a falconet, carrying a three-pound shot, to every point of the gunner's quadrant, each point being the 12th part, or 7° and a half. But from his numbers it is manifest that the piece was not charged with its usual allotment of powder. The result of his trials shews the ranges at the point-blanc, and the several points of elevation, as below.
| Collado's Experiments. | |||
| Elevation at | Range in | ||
| Points. | Deg. | paces. | |
| 0 | or | 0 | 268 |
| 1 | " | 7 1/2 | 594 |
| 2 | " | 15 | 794 |
| 3 | " | 22 1/2 | 954 |
| 4 | " | 30 | 1010 |
| 5 | " | 37 1/2 | 1040 |
| 6 | " | 45 | 1053 |
| 7 | " | 52 1/2 | between the 3d and 4th |
| 8 | " | 60 | between the 2d and 3d |
| 9 | " | 67 1/2 | between the 1st and 2d |
| 10 | " | 75 | between the 0 and 1st |
| 11 | " | 82 1/2 | fell very near the piece. |
The next was by Wm. Bourne, in 1643, in his Art of Shooting in Great Ordnance. His elevations were not regulated by the points of the Gunner's quadrant, but by degrees; and he gives the proportions between the ranges at different elevations and the extent of the pointblanc shot, thus: if the extent of the point-blanc shot be represented by 1, then the proportions of the ranges at several elevations will be as below, viz.
| Bourne's Proportìon of Ranges. | |
| Elevation. | Range. |
| 0° | 1 |
| 5 | 2 2/<*> |
| 10 | 3 1/3 |
| 15 | 4 1/3 |
| 20 | 4 5/6 |
| and the greatest random 5 1/2; |
After him, Eldred and Anderson, both Englishmen, also published treatises on this subject. The former of these was many years gunner of Dover Castle, where most of his experiments were made, the earliest of which are dated in 1611, though his book was not published till 1646, and was intitled The Gunner's Glass. His principles were sufficiently simple, and within certain limits very near the truth, though they were not rigorously so. He has given the actual ranges of different pieces of artillery at small elevations, all under 10 degrees. His experiments are numerous, and appear to be made with great care and caution; and he has honestly set down some, which were not reconcilable to his method: upon the whole he seems to have taken more pains, and to have had a juster knowledge of his business, than is to be found in most of his practical brethren.
Galileo printed his Dialogues on Motion in the year 1646. In these he pointed out the general laws observed by nature in the production and composition of motion, and was the first who described the action and effects of gravity on falling bodies: on these principles he determined, that the flight of a cannon-shot, or of any other projectile, would be in the curve of a parabola, unless so far as it should be diverted from that track by the resistance of the air. He also proposed the means of examining the inequalities which arise from thence, and of discovering what sensible effects that resistance would produce in the motion of a bullet at some given distance from the piece.
Notwithstanding these determinations and hints of Galileo, it seems that those who came after him never imagined that it was necessary to consider how far the operations of Gunnery were affected by this resistance. Instead of this, they boldly asserted, without making the experiment, that no great variation could arise from the resistance of the air in the flight of shells or cannon shot. In this persuasion they supported themselves chiefly by considering the extreme rarity of the air, compared with those dense and ponderous bodies; and at last it became an almost generally established maxim, that the flight of these bodies was nearly in the curve of a parabola.
Thus, Robert Anderson, in his Genuine Use and Effects of the Gunne, published in 1674, and again in his book, To hit a Mark, in 1690, relates a great many experiments; but proceeding on the principles of Galileo, he ftrenuously asserts that the flight of all bullets is in the curve of a parabola; undertaking to answer all objections that could be brought to the contrary. The same thing was also undertaken by Blondel, in his Art de jetter les Bombes, published in 1683; where, after long discussion, he concludes, that the variations from the air's resistance are so slight as not to deserve any notice. The same subject is treated of in the Philos. Trans. N° 216, p. 68, by Dr. Halley; who also, swayed by the very great disproportion between the density of the air and that of iron or lead, thought it reasonable to believe that the opposition of the air to large metal-shot is scarcely discernible; although in small and light shot he owns that it must be accounted for.
But though this hypothesis went on smoothly in speculation; yet Anderson, who made a great number of trials, found it impossible to support it without some new modification. For though it does not appear that he ever examined the comparative ranges of either cannon or musket shot when fired with their usual velocities, yet his experiments on the ranges of shells thrown with velocities that were but sinall, in comparison of those above mentioned, convinced him that their whole track was not parabolical. But instead of making the proper inferences from hence, and concluding that the resistance of the air was of considerable efficacy, he framed a new hypothesis; which was, that the shell or bullet at its first discharge flew to a certain distance in a right line, from the end of which line only it began to describe a parabola: and this right line, which he calls the line of the impulse of the fire, he supposes is the same for all elevations. So that, by assigning a proper length to this line of impulse, it was always in his power to reconcile any two shots made at any two different angles; though the same method could not succeed with three shots; nor indeed does he ever inform us of the event of his experiments when three ranges were tried at one time.
But after the publication of Newton's Principia, it might have been expected, that the defects of the theory would be ascribed to their true cause, which is the great resistance of the air to such swift motions; as in that work he particularly considered the subject of such motions, and related the result of experiments, made on slow motions at least; by which it appeared, that in such motions the resistance increases as the square of the velocities, and he even hints a suspicion that it will increase above that law in swifter motions, as is now known to be the case. So far however were those who treated this subject scientifically, from making a proper allowance for the resistance of the atmosphere, that they still neglected it, or rather opposed it, and their theories still differed most egregiously from the truth. Huygens alone seems to have attended to this principle: for in the year 1690 he published a treatise on gravity, in which he gave an account of some experiments tending to prove that the track of all projectiles, moving with very swift motions, was widely different from that of a parabola. The rest of the learned generally acquiesced in the justness and sufficiency of Galileo's doctrine, and accordingly very erroneous calculations concerning the ranges of cannon were given. Nor was any farther notice taken of these errors till the year 1716, at which time Mr. Ressons, a French officer of artillery, of great merit and experience, gave in a memoir to the Royal Academy, importing that, “although it was agreed that theory joined with practice did constitute the perfection of every art; yet experience had taught him that theory was of very little service in the use of mortars: That the works of M. Blondel had justly enough described the several parabolic lines, according| to the different degrees of the elevation of the piece; but that practice had convinced him there was no theory in the effect of gunpowder; for having endeavoured, with the greatest precision, to point a mortar according to these calculations, he had never been able to establish any solid foundation upon them.”—— One instance only occurs in which D. Bernoulli applies the doctrine of Newton to the motions of projectiles, in the Com. Acad. Petrop. tom. 2, pa. 338 &c. Besides which nothing farther was done in this business till the time of Mr. Benjamin Robins, who published a treatise in 1742, intitled New Principles of Gunnery, in which he treated particularly, not only of the resistance of the atmosphere, but also of the force of gunpowder, the nature and effects of different guns, and almost every thing else relating to the flight of military projectiles; and indeed he carried the theory of gunnery nearly to its utmost perfection.
The sirst thing considered by Mr. Robins, and which is indeed the foundation of all other particulars relating to Gunnery, is the explosive force of gunpowder. M. De la Hire, in the Hist. of the Acad. of Sciences for the year 1702, supposed that this force may be owing to the increased elasticity of the air contained in, and between the grains, in consequence of the heat and fire produced at the time of the explosion: a cause not adequate to the 200th part of the effect. On the other hand, Mr. Robins determined, by irrefragable experiments, that this force was owing to an elastic fluid, similar to our atmosphere, existing in the powder in an extremely condensed state, which being suddenly freed from the powder by the combustion, expanded with an amazing force, and violently impelled the bullet, or whatever may oppose its expansion.
The intensity of this force of exploded gunpowder Mr. Robins ascertained in different ways, after the example of Mr. Hawksbee, related in the Philos. Trans. N° 295, and his Physico-Mechan. Exper. pa. 81. One of these is by firing the powder in the air thus: A small quantity of the powder is placed in the upper part of a glass tube, and the lower part of the tube is immerged in water, the water being made to rise so near the top, that only a small portion of air is left in that part where the powder is placed: then in this situation the communication between the upper part of the tube and the external air being closed, the powder is fired by means of a burning glass, or otherwise; the water descends upon the explosion, and stands lower in the tube than before, by a space proportioned to the quantity of powder fired.
Another way was by firing the powder in vacuo, viz, in an exhausted receiver, by dropping the grains of powder upon a hot iron included in the receiver. By this means a permanent elastic fluid was generated from the fired gunpowder, and the quantity of it was always in proportion to the quantity of powder that was used, as was found by the proportional sinking of the mercurial gage annexed to the air pump. The result of these experiments was, that the weight of the elastic air thus generated, was equal to 3/10 of the compound mass of the gunpowder which yielded it; and that its bulk, when cold and expanded to the rarity of common atmospheric air, was about 240 times the bulk of the powder; and consequently in the same proportion would such fluid at first, if it were cold, exceed the force or clasticity of the atmosphere. But as Mr. Robins found, by another ingenious-experiment, that air heated to the extreme degree of the white heat of iron, has its elasticity quadrupled, or is 4 times as strong; he thence inferred that the force of the elastic air generated as above, at the moment of the explosion, is at least 4 times 240, or 960, or in round numbers about 1000 times as strong as the elasticity or pressure of the atmosphere, on the same space.
Having thus determined the force of the gunpowder, or intensity of the agent by which the projectile is to be urged, Mr. Robins next proceeds to determine the effects it will produce, or the velocity with which it will impel a shot of a given weight from a piece of ordnance of given dimensions; which is a problem strictly limited, and perfectly soluble by mathematical rules, and is in general this: Given the first force, and the law of its variation, to determine the velocity with which it will impel a given body in passing through a given space, which is the length of the bore of the gun.
In the solution of this problem, Mr. Robins assumes these two postulates, viz, 1, That the action of the powder on the bullet ceases as soon as the bullet is out of the piece; and 2d, That all the powder of the charge is fired and converted into elastic fluid before the bullet is sensibly moved from its place: assumptions which for good reasons are found to be in many cases very near the truth. It is to be noted also, that the law by which the force of the elastic fluid varies, is this, viz, that its intensity is directly as its density, or reciprocally proportional to the space it occupies, being so much the stronger as the space is less: a principle well known, and common to all elastic fluids. Upon these principles then Mr. Robins resolves this problem, by means of the 39th prop. of Newton's Principia in a direct way, and the result is equivalent to this theorem, when the quantities are expressed by algebraic symbols; viz, the velocity of the ball where v is the velocity of the ball, a the length of the charge of powder, b the whole length of the bore, c the spec. grav. of the ball, or wt. of a cubic foot of the same matter in ounces, d the diam. of the bore, w the wt. of the ball in ounces.
For example, Suppose a = 2 5/8 inc., b = 45 inches, c = 11345 oz, for a ball of lead, and d = 3/4 inches; then feet per second, the velocity of the ball.
Or, if the wt. of the bullet be w = 1 9/20 oz = 20/20 oz. Then feet, as before.
“Having in this proposition, says Mr. Robins, shewn how the velocity, which any bullet acquires from| the force of powder, may be computed upon the principles of the theory laid down in the preceding propositions; we shall next shew, that the actual velocities, with which bullets of different magnitudes are impelled from different pieces, with different quantities of powder, are really the same with the velocities assigned by these computations; and consequently that this theory of the force of powder, here delivered, does unquestionably ascertain the true action and modification of this enormous power.
“But in order to compare the velocities communicated to bullets by the explosion with the velocities resulting from the theory by computation; it is necessary that the actual velocities with which bullets move, should be capable of being discovered, which yet is impossible to be done by any methods hitherto made public. The only means hitherto practised by others for that purpose, have been either by observing the time of the flight of the shot through a given space, or by measuring the range of the shot at a given elevation; and thence computing, on the parabolic hypothesis, what velocity would produce this range. The first method labours under this insurmountable difficulty, that the velocities of these bodies are often so swift, and consequently the time observed is so short, that an imperceptible error in that time may occasion an error in the velocity thus found, of 2, 3, 4, 5, or 600 feet in a second. The other method is so fallacious, by reason of the resistance of the air (to which inequality the first is also liable), that the velocities thus assigned may not be perhaps the 10th part of the actual velocities sought.
“To remedy then these inconveniences, I have invented a new method of finding the real velocities of bullets of all kinds; and this to such a degree of exactness (which may be augmented too at pleasure), that in a bullet moving with a velocity of 1700 feet in 1″, the error in the estimation of it need never amount to its 500th part; and this without any extraordinary nicety in the construction of the machine.”
Mr. Robins then gives an account of the machine by which he measures the velocities of the balls, which machine is simply this, viz, a pendulous block of wood suspended freely by a horizontal axis, against which block are to be fired the balls whose velocities are to be determined.
“This instrument thus fitted, if the weight of the pendulum be known, and likewise the respective distances of its centre of gravity, and of its centre of oscillation, from its axis of suspension, it will thence be known what motion will be communicated to this pendulum by the percussion of a body of a known weight moving with a known degree of celerity, and striking it in a given point; that is, if the pendulum be supposed at rest before the percussion, it will be known what vibration it ought to make in consequence of such a determined blow; and, on the contrary, if the pendulum, being at rest, is struck by a body of a known weight, and the vibration, which the pendulum makes after the blow, is known, the velocity of the striking body may from thence be determined.
“Hence then, if a bullet of a known weight strikes the pendulum, and the vibration, which the pendulum makes in consequence of the stroke, be ascertained; the velocity with which the ball moved, is thence to be known.”
Mr. Robins then explains his method of computing velocities from experiments with this machine; which method is rather troublesome and perplexed, as well as the rules of Euler and Antoni, who followed him in this business, but a much simpler rule is given in my Tracts, vol. 1, p. 119, where such experiments are explained at full length, and this rule is expressed by either of the two following formulas, , the velocity; where v denotes the velocity of the ball when it strikes the pendulum, p the weight of the pendulum, b the weight of the ball, c the chord of the arc described by the vibration to the radius r, g the distance below the axis of motion to the centre of gravity, o the distance to the centre of oscillation, i the distance to the point of impact, and n the number of oscillations the pendulum will perform in one minute, when made to oscillate in small arcs. The latter of these two theorems is much the easiest, both because it is free of radicals, and because the value of the radical √o, in the former, is to be first computed from the number n, or number of oscillations the pendulum is observed to make.
With such machines Mr. Robins made a great number of experiments, with musket barrels of different lengths, with balls of various weights, and with different charges or quantities of powder. He has set down the results of 61 of these experiments, which nearly agree with the corresponding velocities as computed by his theory of the force of powder, and which therefore establish that theory on a sure foundation.
From these experiments, as well as from the preceding theory, many important conclusions were deduced by Mr. Robins; and indeed by means of these it is obvious that every thing may be determined relative both to the true theory of projectiles, and to the practice of artillery. For, by firing a piece of ordnance, charged in a similar manner, against such a ballistic pendulum from different distances, the velocity lost by passing through such spaces of air will be found, and consequently the resistance of the air, the only circumstance that was wanting to complete the theory of Gunnery, or military projectiles; and of this kind I have since made a great number of experiments with cannon balls, and have thereby obtained the whole series of resistances to such a ball when moving with every degree of velocity, from 0 up to 2000 feet per second of time. In the structure of artillery, they may likewise be of the greatest use: For hence may be determined the best lengths of guns; the proportions of the shot and powder to the several lengths; the thickness of a piece, so as it may be able to confine, without bursting, any given charge of powder; as also the effect of wads, chambers, placing of the vent, ramming the powder, &c. For the many other curious circumstances relating to this subject, and the various other improvements in the theory and practice of Gunnery, made by Mr. Robins, consult the first vol. of his Tracts, collected and published by Dr. Wilson, in the year 1761, where ample information may be found.
Soon after the first publication of Robins's New Principles of Gunnery, in 1742, the learned in several| other nations, treading in his steps, repeated and farther extended the same subject, sometimes varying and enlarging the machinery; particularly Euler in Germany, D'Antoni in Italy, and Messrs. D'Arcy and Le Roy in France. But most of these, like Mr. Robins, with small fire-arms, such as muskets, and fusils.
But in the year 1775, in conjunction with several able officers of the Royal Artillery, and other ingenious gentlemen, I undertook a course of experiments with the ballistic pendulum, in which we ventured to extend the machinery to cannon shot of 1, 2, and 3 pounds weight. An account of these experiments was published in the Philos. Trans. for 1778, and for which the Royal Society honoured me with the prize of the gold medal. “These were the only experiments that I know of which had been made with cannon balls for this purpose, although the conclusions to be deduced from such, are of the greatest importance to those parts of natural philosophy which are dependent on the effects of fired gunpowder; nor do I know of any other practical method of ascertaining the initial velocities within any tolerable degree of the truth. The knowledge of this velocity is of the utmost consequence in Gunnery: by means of it, together with the law of the resistance of the medium, every thing is determinable relative to that business; for, besides its being an excellent method of trying the strength of different sorts of powder, it gives us the law relative to the different quantities of powder, to the different weights of shot, and to the different lengths and sizes of guns. Besides these, there does not seem to be any thing wanting to answer any inquiry that can be made concerning the flight and ranges of shot, except the effects arising from the resistance of the medium. In these experiments the weights of the pendulums employed were from 300 to near 600 pounds. In that paper is described the method of constructing the machinery, of finding the centres of gravity and oscillation of the pendulum, and of making the experiments, which are all set down in the form of a journal, with all the minute and concomitant circumstances; as also the investigation of the new and easy rule, set down just above, for computing the velocity of the ball from the experiments. The charges of powder were varied from 2 to 8 ounces, and the shot from 1 to near 3 pounds. And from the whole were clearly deduced these principal inferences, viz,
“1. First, That gunpowder fires almost instantaneously.—2. That the velocities communicated to balls or shot, of the same weight, by different quantities of powder, are nearly in the subduplicate ratio of those quantities: a small variation, in defect, taking place when the quantities of powder became great.—3. And when shot of different weights are employed, with the same quantity of powder, the velocities communicated to them, are nearly in the reciprocal subduplicate ratio of their weights.—4. So that, universally, shot which are of different weights, and impelled by the firing of different quantities of powder, acquire velocities which are directly as the square roots of the quantities of powder, and inversely as the square roots of the weights of the shot, nearly.—5. It would therefore be <*> great improvement in artillery, to make use of shot of <*> long form, or of heavier matter; for thus the mo- mentum of a shot, when fired with the same weight of powder, would be increased in the ratio of the square root of the weight of the shot.—6. It would also be an improvement to diminish the windage; for by so doing, one-third or more of the quantity of powder might be saved.—7. When the improvements mentioned in the last two articles are considered as both taking place, it is evident that about half the quantity of powder might be saved, which is a very considerable object. But important as this saving may be, it seems to be still exceeded by that of the article of the guns; for thus a small gun may be made to have the effect and execution of another of two or three times its size in the present mode, by discharging a shot of two or three times the weight of its natural ball or round shot. And thus a small ship might discharge shot as heavy as those of the greatest now made use of.
“Finally, as the above experiments exhibit the regulations with regard to the weights of powder and balls, when fired from the same piece of ordnance, &c; so by making similar experiments with a gun, varied in its length, by cutting off from it a certain part before each course of experiments, the effects and general rules for the different lengths of guns may be certainly determined by them. In short, the principles on which these experiments were made, are so fruitful in consequences, that, in conjunction with the effects resulting from the resistance of the medium, they seem to be sufsicient for answering all the enquiries of the speculative philosopher, as well as those of the practical artillerist.
In the year 1786 was published the first volume of my Tracts, in which is detailed, at great length, another very extensive course of experiments which were carried on at Woolwich in the years 1783, 1784, and 1785, by order of the Duke of Richmond, Master Genearl of the Ordnance. The objects of this course were very numerous, but the principal of them were the following:
“1. The velocities with which balls are projected by equal charges of powder, from pieces of the same weight and calibre, but of different lengths.
“2. The velocities with different charges of powder, the weight and length of the gun being the same.
“3. The greatest velocity due to the different lengths of guns, to be obtained by increasing the charge as far as the resistance of the piece is capable of sustaining.
“4. The effect of varying the weight of the piece; every thing else being the same.
“5. The penetration of balls into blocks of wood.
“6. The ranges and times of flight of balls; to compare them with their initial velocities for determining the resistance of the medium.
“7. The effect of wads; of different degrees of ramming; of different degrees of windage; of different positions of the vent; of chambers, and trunnions, and every other circumstance necessary to be known for the improvement of artillery.”
All these objects were obtained in a very perfect and accurate manner; excepting only the article of ranges, which were not quite so regular and uniform as might| be wished. The balls too were most of them of one pound weight; but the powder was increased from 1 ounce, up till the bore was quite full; and the pendulum was from 600 to 800lb. weight. The conclusions from the whole were as follow:
“1. That the former law, between the charge and velocity of ball, is again confirmed, viz, that the velocity is directly as the square root of the weight of powder, as far as to about the charge of 8 ounces: and so it would continue for all charges, were the guns of an indefinite length. But as the length of the charge is increased, and bears a more considerable proportion to the length of the bore, the velocity falls the more short of that proportion.
“2. That the velocity of the ball increases with the charge to a certain point, which is peculiar to each gun, where it is greatest; and that by farther increasing the charge, the velocity gradually diminishes, till the bore is quite full of powder. That this charge for the greatest velocity is greater as the gun is longer, but not greater however in so high a proportion as the length of the gun is, so that the part of the bore filled with powder bears a less proportion to the whole in the long guns, than it does in the short ones; the part of the whole which is filled being indeed nearly in the reciprocal subduplicate ratio of the length of the empty part. And the other circumstances are as in this table.
| Table of Charges producing the Greatest Velocity. | ||||
| Gun Num. | Length of the bore. | Length filled. | Part of the whole. | Wt. of the powder. |
| inches. | inches. | oz. | ||
| 1 | 28.2 | 8.2 | 3/10 | 12 |
| 2 | 38.1 | 9.5 | 3/12 | 14 |
| 3 | 57.4 | 10.7 | 3/1<*> | 16 |
| 4 | 79.9 | 12.1 | 3/20 | 18 |
“3. It appears that the velocity continually increases as the gun is longer, though the increase in velocity is but very small in respect of the increase in length, the velocities being in a ratio somewhat less than that of the square roots of the length of the bore, but somewhat greater than that of the cube roots of the length, and is indeed nearly in the middle ratio between the two.
“4. The range increases in a much less ratio than the velocity, and indeed is nearly as the square root of the velocity, the gun and elevation being the same. And when this is compared with the property of the velocity and length of gun in the foregoing paragraph, we perceive that very little is gained in the range by a great increase in the length of the gun, the charge being the same. And indeed the range is nearly as the 5th root of the length of the bore; which is so small an increase, as to amount only to about 1/7th part more range for a double length of gun.
“5. It also appears that the time of the ball's flight is nearly as the range; the gun and elevation being the same.
“6. It appears that there is no sensible difference caused in the velocity or range, by varying the weight of the gun, nor by the use of wads, nor by different degrees of ramming, nor by firing the charge of powder in different parts of it.
“7. But a great difference in the velocity arises from a small degree of windage. Indeed with the usual established windage only, namely, about 1/20th of the caliber, no less than between 1/3 and 1/4 of the powder escapes and is lost. And as the balls are often smaller than that size, it frequently happens that half the powder is lost by unnecessary windage.
“8. It appears that the resisting force of wood, to balls fired into it, is not constant. And that the depths penetrated by different velocities or charges, are nearly as the logarithms of the charges, instead of being as the charges themselves, or, which is the same thing, as the square of the velocity.
“9. These, and most other experiments, shew that balls are greatly deflected from the direction they are projected in; and that so much as 300 or 400 yards in a range of a mile, or almost 1/4th of the range, which is nearly a deflection of an angle of 15 degrees.
“10. Finally, these experiments furnish us with the following concomitant data, to a tolerable degree of accuracy, namely, the dimensions and elevation of the gun, the weight and dimensions of the powder and shot, with the range and time of flight, and the first velocity of the ball. From which it is to be hoped that the measure of the resistance of the air to projectiles, may be determined, and thereby lay the foundation for a true and practical system of Gunnery, which may be as well useful in service as in theory.”
Since the publication of those Tracts, we have prosecuted the experiments still farther, from year to year, gradually extending our aim to more objects, and enlarging the guns and machinery, till we have arrived at experiments with the 6 pounder guns, and pendulums of 1800 pounds weight. One of the new objects of enquiry, was the resistance the atmosphere makes to military projectiles; to obtain which, the guns have been placed at many different distances from the pendulum, against which they are fired, to get the velocity lost in passing through those spaces of air; by which, and the use of the whirling machine, described near the end of the 1st vol. of Robins's Tracts, for the slower motions, I have investigated the resistance of the air to given balls moving with all degrees of velocity, from 0 up to 2000 feet per second<*> as well as the resistance for many degrees of velocity, to planes and figures of other shapes, and inclined to their path in all varieties of angles; from which I have deduced general laws and formulas for all such motions.
Mr. Robins made also similar experiments on the resistance of the air; but being only with musket bullets, on account of their smallness, and of their change of figure by the explosion of the powder, I find they are very inaccurate, and considerably different from those above mentioned, which were accurately made with pretty considerable cannon balls, of iron. For which reason we may omit here the rules and theory deduced from them by Mr. Robins, till others more correct shall| have been established. All these experiments indeed agree in evincing the very enormous resistance the air makes to the swift motions of military projectiles, amounting in some cases to 20 or 30 times the weight of the ball itself; on which account the common rules for projectiles, deduced from the parabolic theory, are of little or no use in real practice; for, from these experiments it is clearly proved, that the track described by the flight even of the heaviest shot, is neither a parabola, nor yet approaching any thing near it, except when they are projected with very small velocities; in so much that some balls, which in the air range only to the distance of one mile, would in vacuo, when projected with the same velocity, range above 10 or 20 times as far. For the common rules of the parabolic theory, see Projectiles. And for a small specimen of my experiments on resistances, see the 2d vol. of the Edinburgh Philos. Trans.; as also my Conic Sections and Select Exercises, at the end, also the articles Force, and Resistance, in this Dictionary.
Mr. Benjamin Thompson instituted a <*>ry considerable course of experiments of the same kind as those of Mr. Robins, with musket barrels, which was published in the Philos. Trans. vol. 71, for the year 1781. In these experiments, the conclusions of Mr. Robins are generally confirmed, and several other curious circumstances in this business are remarked by Mr. Thompson. This gentleman also pursues a hint thrown out by Mr. Robins relative to the determining the velocity of a ball from the recoil of the pendulous gun itself. Mr. Robins, in prop. 11, remarks that the effect of the exploded powder upon the recoil of the gun, is the same, whether the gun is charged with a ball, or without one; and that the chord, or velocity, of recoil with the powder alone, being subtracted from that of the recoil when charged with both powder and ball, leaves the velocity which is due to the ball alone. From whence Mr. Thompson observes, that the inference is obvious, viz, that the momentum thus communicated to the gun by the ball alone, being equal to the momentum of the ball, this becomes known; and therefore being divided by the known weight of the ball, the quotient will be its velocity. Mr. Thompson sets a great value on this new rule, the velocities by means of which, he found to agree nearly with several of those deduced from the motion of the pendulum; and in the other cases in which they differed greatly from these, he very inconsistently supposes that these latter ones are erroneous. In the experiments however contained in my Tracts, a great multitude of those cases are compared together, and the inaccuracy of that new rule is fully proved.
Having in the 9th prop. compared together a number of computed and experimented velocities of balls, to verify his theory: in the 10th prop. Mr. Robins assigns the changes in the force of powder, which arise from the different state of the atmosphere, as to heat and moisture, both which he finds have some effect on it, but especially the latter. In prop. 11 he investigates the velocity which the flame of gunpowder acquires by expanding itself, supposing it fired in a given piece of artillery, without either a bullet or any other body before it. This velocity he finds is upwards of 7000 feet per second. But the celebrated Euler, in his commentary on this part of Mr. Robins's book, thinks it may be still much greater. And in this prop. too it is that Mr. Robins declares his opinion, above alluded to, viz, that the effect of the powder upon the recoil of the gun is the same, in all cases, whether fired with a ball, or without one.—In prop. 12 he ascertains the manner in which the flame of powder impels a ball which is laid at a considerable distance from the charge; shewing here that the sudden accumulation and density of the fluid against the ball, is the reason that the barrel is so often burst in those cases.—In prop. 13 he enumerates the various kinds of powder, and describes the properest methods of examining its goodness. He here shews that the best proportion of the ingredients, is when the saltpetre is 3/4 of the whole compound mass of the powder, and the sulphur and charcoal the other 1/4 between them, in equal quantities. In this prop. Mr. Robins takes occasion to remark upon the use of eprouvettes, or methods of trying powder; condemning the practice of the English in using what is called the vertical eprouvette; as well as that of the French, in using a small mortar, with a very large ball, and a small charge of powder: and instead of these, he strongly recommends the use of his ballistic pendulum, for its great accuracy: But for still more dispatch, he says he should use another method, which however he reserves to himself, without giving any particular description of it. From what has been done by Mr. Robins upon this head, several persons have introduced his method of suspending the gun as a pendulum, and noting the quantity of its oscillating recoil when fired with a certain quantity of powder; and of this kind I have contrived a machine, which possesses several advantages over all others, being extremely simple, accurate, and expeditious; so much so indeed, that the weighing out of the powder is the chief part of the trouble. See Gunpowder, and Eprouvette.
The other or 2d chapter of Mr. Robins's work, in 8 propositions, treats “of the resistance of the air, and of the track described by the flight of shot and shells.” And of these, prop. 1 describes the general principles of the resistance of fluids to solid bodies moving in them. Here Mr. Robins discriminates between continued and compressed fluids, which immediately rush into the space quitted by a body moving in them, and whose parts yield to the impulse of the body without condensing and accumulating before it; and such fluids as are imperfectly compressed, rushing into a void space with a limited velocity, as in the case of our atmosphere, which condenses more and more before the ball as this moves quicker, and also presses the less behind it, by following it always with only a given velocity: hence it happens that the former fluid will resist moving bodies in proportion to the square of the velocity, while the latter resists in a higher proportion.—Proposition 2 is “to determine the resistance of the air to projectiles by experiments.” One of the methods for this purpose, is by the ballistic pendulum, placing the gun at different distances from it, by which he finds the velocity lost in passing through certain spaces of air, and consequently the force of resistance to such velocities as the body moves with in the several parts of its path. And another way was by firing balls, with a known given velocity, over a large piece of water, in which the fall and plunge of the ball| could be seen, and consequently the space it passed over in a given time. By these means Mr. Robins determined the resistances of the air to several different velocities, all which shewed that there was a gradual increase of the resistance, over the law of the square of the velocity, as the body moved quicker.—In the remaining propositions of this chapter, he proceeds a little farther in this subject of the resistance of the air; in which he lays down a rule for the proportion of the resistance between two assigned velocities; and he shews that when a 24 pound ball, fired with its full charge of powder, first issues from the piece, the resistance it meets with from the air is more than 20 times its weight. He farther shews that “the track described by the flight of shot or shells is neither a parabola, nor nearly a parabola, unless they are projected with small velocities;” and that “bullets in their flight 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: and in the 8th or last proposition, he pretends to shew that the depths of penetration of balls into firm substances, are as the squares of the velocities. But this is a mistake; for neither does it appear that his trials were sufficiently numerous or various, nor were his small leaden balls fit for this purpose; and I have found, from a number of trials with iron cannon balls, that the penetrations are in a much lower proportion, and that the resisting force of wood is not uniform. See my Tracts.
In the following small tracts, added to the principles, in this volume, Mr. Robins prosecutes the subject of the resistance of the air much farther, and lays down rules for computing ranges made in the air. But these must be far from accurate, as they are founded on the two following principles, which I know, from numerous experiments, are erroneous: viz, 1st, “That till the velocity of the projectile surpasses that of 1100 feet in a second, the resistance may be esteemed to be in the duplicate proportion of the velocity. 2d, That if the velocity be greater than that of 11 or 1200 feet in a second, then the absolute quantity of that resistance in these greater velocities will be near 3 times as great, as it should be by a comparison with the smaller velocities.” For, instead of leaping at once from the law of the square of the velocities, and ever after being about 3 times as much, my experiments prove that the increase of the resistance above the law of the square of the velocity, takes place at first in the smallest motions, and increases gradually more and more, to a certain point, but never rises so high as to be 3 times that quantity, after which it decreases again. To render this evident, I have inserted the following table of the actual quantities of resistances, which are deduced from accurate experiments, and which shew also the nature of the law of the variations, by means of the columns of differences annexed; reserving the detail of the experiments themselves to another occasion. These resistances are, upon a ball of 1.965 inc. diameter, in avoirdupois ounces, and are for all velocities, from 0, up to that of 2000 feet per second of time.
| Veloc. in feet | Resist. in ounces | 1st Differenes | 2d Differences |
| 0 | 0.000 | ||
| 5 | 0.006 | ||
| 10 | 0.025 | ||
| 15 | 0.054 | ||
| 20 | 0.100 | ||
| 25 | 0.155 | ||
| 30 | 0.23 | ||
| 40 | 0.42 | ||
| 50 | 0.67 | ||
| 100 | 2 3/4 | ||
| 8 1/4 | |||
| 200 | 11 | 5 3/4 | |
| 14 | |||
| 300 | 25 | 6 | |
| 20 | |||
| 400 | 45 | 7 | |
| 27 | |||
| 500 | 72 | 8 | |
| 35 | |||
| 600 | 107 | 9 | |
| 44 | |||
| 700 | 151 | 10 | |
| 54 | |||
| 800 | 205 | 12 | |
| 66 | |||
| 900 | 271 | 13 | |
| 79 | |||
| 1000 | 350 | 13 | |
| 92 | |||
| 1100 | 442 | 12 | |
| 104 | |||
| 1200 | 546 | 11 | |
| 115 | |||
| 1300 | 661 | 9 | |
| 124 | |||
| 1400 | 785 | 7 | |
| 131 | |||
| 1500 | 916 | + 4 | |
| 135 | |||
| 1600 | 1051 | 0 | |
| 135 | |||
| 1700 | 1186 | - 2 | |
| 133 | |||
| 1800 | 1319 | 5 | |
| 128 | |||
| 1900 | 1447 | 6 | |
| 122 | |||
| 2000 | 1569 |
The additional tracts of Mr. Robins, in the latter part of this volume, which contain many useful and important matters, are numbered and titled as follows, viz, Number 1, “Of the resistance of the air. Number 2, Of the resistance of the air; together with the method of computing the motions of bodies projected in that medium. Number 3, An account of the experiments, relating to the resistance of the air, exhibited at different times before the Royal Society, in the year 1746. Number 4, Of the force of fired gunpowder, together with the computation of the velocities thereby communicated to military projectiles. Number 5, A comparison of the experimental ranges of cannon and mortars with the theory contained in the preceding papers.—Practical Maxims relating to the effects and management of artillery, and the flight of shells and shot.—A proposal for increasing the strength of the British navy, by changing all the guns, from the 18 pounders downwards, into others of equal weight, but of a greater bore.” With several letters, and other papers, “On pointing, or the directing of cannon to strike distant objects; Of the nature and advantage of reifled barrel picces,” &c.|
I have dwelt thus long on Mr. Robins's New Principles of Gunnery, because it is the first work that can be considered as attempting to establish a practical system of gunnery, and projectiles, on good experiments, on the force of gunpowder, on the resistance of the air, and on the effects of different pieces of artillery. Those experiments are however not sufficiently perfect, both on account of the smallness of the bullets, and for want of good ranges, to form a proper theory upon. I have supplied some of the necessary desiderata for this purpose, viz, the resistance of the air to cannon balls moving with all degrees of velocity, and the velocities communicated by given charges of powder to different balls, and from different pieces of artillery. But there are still wanting good experiments with different pieces of ordnance, giving the ranges and times of flight, with all varieties of charges, and at all different angles of elevation. A few however of those I have obtained, as in the following small table, which are derived from experiments made with a medium onepounder gun, the iron ball being nearly 2 inches in diameter.
| Powder | Elev. of gun | Veloc. of ball | Range | Time of flight |
| oz | ° | feet | feet | ″ |
| 2 | 15 | 860 | 4100 | 9 |
| 4 | 15 | 1230 | 5100 | 12 |
| 8 | 15 | 1640 | 6000 | 14 1/2 |
| 12 | 15 | 1680 | 6700 | 15 1/2 |
| 2 | 45 | 860 | 5100 | 21 |
The celebrated Mr. Euler added many excellent dissertations on the subject of Gunnery, in his translation of Robins's Gunnery into the German language; which were again farther improved in Brown's translation of the same into English in the year 1777. See also Antoni's Examen de la Poudre; the experiments of MM. D'Arcy and Le Roy, in the Memoirs of the Academy in 1751; and D'Arcy's Essai d'une theorie d'artillerie in 1760: my Tracts; and paper on the force of fired gunpowder in the Philof. Trans. for 1778: and Thompson's paper on the same subject in 1781. Of the common or parabolic theory of Gunnery, Mr. Simpson gave a very neat and concise treatise in his Select Exercises. And other authors on this part, are Starrat, Gray, Williams, Glenie, &c.
