in botany; a genus of the diandria order, belonging to the gynandra clasps of plants. The amentum consists of uniflorous scales; there is neither calyx nor corolla; the germen is bidentated, with two styles and one seed.

IS the art of charging, directing, and exploding firearms, as cannons, mortars, muskets, &c. to the best advantage.—As this art depends greatly on having the guns and shot of a proper size and figure, and well adapted to each other, it hence follows that the proper dimensions, &c. of cannon and small arms come properly to be considered under the present article.

Sect. I. History of Gunnery.

The ancients, who knew not the use of gunpowder and fire-arms, had notwithstanding machines which were capable of discharging stones, darts, and arrows, with great force. These were actuated chiefly by the elastic force of ropes, or of strong springs, and required a great number of men to work them; for which reason, the explosion of gunpowder, as acting instantaneously, and seemingly with irresistible force, seemed to be a most proper succedaneum for all the powers by which the military engines in former times were actuated. It soon appeared, however, that this force was not very easily applied. Though the experiment of Bartholomew Schwartz, mentioned under the article Gun, had given a good hint towards this application in a successful manner, yet the violent reaction of the inflamed powder on the containing vessels rendered them very apt to burst, to the great danger of those who stood near them. The gunpowder in those days, therefore, was much weaker than it is now made; though this proved a very insufficient remedy for the inconvenience above mentioned. It was also 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. Thus they were capable of enduring greater charges of a better powder than what had been formerly used; and their iron-bullets (which were from 40 to 60 pounds weight), being impelled with greater velocities, were more effectual than the heaviest stones could ever prove. This change took place about the latter end of the 15th century.

By this means powder compounded in the manner now practised over all Europe came first into use. But the change of the proportion of materials was not the only improvement it received. The method of graining it is undoubtedly a considerable advantage. At first the powder was always in the form of fine meal, such as it was reduced to by grinding the materials together. 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 made use of for cannon. But at last the additional strength which the grained powder was found to acquire from the free passage of the air between the grains, occasioned the meal-powder to be entirely laid aside.

For the last two hundred years, the formation of cannon hath been very little improved; the best pieces of modern artillery differing little in their proportions from those used in the time of Charles V. Indeed lighter and shorter pieces have been often proposed and essayed; but though they have their advantages in particular cases, yet it seems now to be agreed that they are altogether insufficient for general service. But though the proportions of the pieces have not been much varied within that period, yet their use and application have undergone considerable alterations; the same ends being now accomplished by smaller pieces than what were formerly thought necessary. Thus the battering cannon now universally approved of are those formerly called demi-cannons, carrying a ball of 24 pounds weight; it being found by experience, that their stroke, though less violent than that of larger pieces, is yet sufficiently adapted to the strength of the usual profiles of fortification; and that the facility of their carriage and management, and the ammunition they spare, give them great advantages beyond the whole cannons formerly employed in making breaches. 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 beat down, seems also 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 so that the bullet may just go clear of the parapet of the enemy, and drop into their works. By this means the bullet, coming to the ground at a small angle, and with a small velocity, does not bury itself, but bounds or rolls along in the direction in which it was fired; and therefore, if the piece be placed in a line with the battery it is intended to silence, or the front it is to sweep, each shot rakes the whole length of that battery or front; and has thereby a much greater chance of disabling the defendants, and dismounting their cannon, than it would have if fired in the common manner. This method was invented by Vauban, and was by him styled Batterie à Ricochet. It was first put in practice in the year 1692 at the siege of Aeth.—Something similar to this was put in practice by the king of Prussia at the battle of Roßbach in 1757. He had several five-inch mortars, made with trunions and mounted on travelling carriages, which fired obliquely on the enemy's lines, and amongst their horse. They were charged with eight ounces of powder, and elevated at an angle of one degree fifteen minutes, and did great execution; for the shells rolling along the lines with burning fuses made the stoutest of the enemy not wait for their bursting.

Sect. II. Theory of Gunnery.

The use of fire-arms had been known for a long time before any theory concerning them was attempted. The first author who wrote professedly on the flight of cannon-shot was Tartalea. In 1537 he published a book, at Venice, intitled Nova Scientia; and afterwards another, intitled Questi et Inventioni diversi, printed at the same place in 1546, in which he treats professedly on these motions. His discoveries were but few, on account of the imperfect state of mechanical knowledge at that time. However, he determined, that the greatest range of cannon was with an elevation of 45 degrees. He likewise determined, (contrary to the opinion of practitioners), that no part of the tract described by a bullet was a right line; although the curvature was in some cases so little, that it was not attended to. He compared it to the surface of the sea; which, though it appears to be a plane, is yet undoubtedly incurvated round the centre of the earth. He also affirms to himself the invention of the gunner's quadrant, and often gave shrewd guesses at the event of some untried methods. But as he had not opportunities of being conversant in the practice, and founded his opinions only on speculation, he was condemned by most of the succeeding writers, though often without any sufficient reason. The philosophers of those times also intermeddled in the questions hence arising; and many disputes on motion were set on foot (especially in Italy), which continued till the time of Galileo, and probably gave rise to his celebrated Dialogues on motion. These were published in the year 1638; but in this interval, and before Galileo's doctrine was thoroughly established, many theories of the motion of military projectiles, and many tables of their comparative ranges at different elevations, were published; all of them egregiously fallacious, and utterly irreconcilable with the motions of these bodies. Very few of the ancients indeed refrained from indulging themselves in speculations concerning the difference between natural, violent, and mixed motions; although scarce any two of them could agree in their theories.

It is strange, however, that, during all these experiments, so few of those who were intrusted with the charge of artillery thought it worth while to bring persons on these theories to the test of experiment. Mr Robin informs us, in his Preface to the New Principles of artillery, Gunnery, that he had met with no more than four authors who had treated on this subject. The first of these is Collado, who has given the ranges of a falconet carrying a three-pound shot to each point of the gunner's quadrant. But from his numbers it is manifest, that the piece was not charged with its customary allotment of gun-powder. The results of his trials were, that the point-blank shot, or that in which the path of the ball did not sensibly deviate from a right line, extended 268 paces. At an elevation of one point (or \( \frac{7}{2} \) of the gunner's quadrant) the range was 594 paces; at an elevation of two points, 794 paces; at three points, 954 paces; at four, 1010; at five, 1040; and at six, 1053 paces. At the seventh point, the range fell between those of the third and fourth; at the eighth point, it fell between the ranges of the second and third; at the ninth point, it fell between the ranges of the first and second; at the tenth point, it fell between the point-blank distance and that of the first point; and at the eleventh point, it fell very near the piece.—The paces spoke of by this author are not geometrical ones, but common steps.

The year after Collado's treatise, another appeared on the same subject by one Bourne an Englishman. His elevations were not regulated by the points of the gunner's quadrant, but by degrees; and he afterwards the proportions between the ranges at different elevations and the extent of point-blank shot. According to him, if the extent of the point-blank shot be represented by 1, the range at 5° elevation will be \( \frac{2}{3} \); at 10° it will be \( \frac{3}{4} \); at 15° it will be \( \frac{4}{5} \); at 20° it will be \( \frac{5}{6} \), and the greatest range will be \( \frac{5}{6} \). This last, he tells us, is in a calm day when the piece is elevated to 42°; but according to the strength of the wind, and as it favours or opposes the flight of the shot, it may be from 45° to 36°.—He hath not informed us with what piece he made his trials; though by his proportions it seems to have been a small one. This however ought to have been attended to, as the relation between the extent of different ranges varies extremely according to the velocity and density of the bullet.

After him Eldred and Anderson, both Englishmen, published treatises on this subject. The first pub- lished his treatise in 1646, and has given the actual ranges of different pieces of artillery at small elevations all under ten degrees. His principles were not rigorously true, though not liable to very considerable errors; yet, in consequence of their deviation from the truth, he found it impossible to make some of his experiments agree with his principles.

In 1638, Galileo printed his dialogues on motion. 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 any other projectile, would be in the curve of a parabola, except in so far as it was diverted from that track by the resistance of the air. He has 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.

Though Galileo had thus shown, that, independent of the resistance of the air, all projectiles would, in their flight, describe the curve of a parabola; yet those who came after him, seem never to have imagined that it was necessary to consider how far the operations of gunnery were affected by this resistance. The subsequent writers indeed boldly asserted, without making the experiment, that no considerable variation could arise from the resistance of the air in the flight of shells or cannon shot. In this persuasion they supposed 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.

In 1674, Mr Anderson above-mentioned published his treatise on the nature and effects of the gun; in which he proceeds on the principles of Galileo, and strenuously 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 Mr Blondel, in a treatise published at Paris in 1683; where, after long discussion, the author concludes, that the variations from the air's resistance are so slight as scarcely to merit notice. The same subject is treated of in the Philosophical Transactions, N. 216, p. 68, by Dr Halley; and he also, swayed by the very great disproportion between the density of the air and that of iron or lead, thinks 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 small velocities (in comparison of those above-mentioned), convinced him that their whole tract was not parabolical. But instead of making the proper inferences from hence, and concluding the resistance of the air to be 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 impulse of the fire, he supposes to be the same in all elevations. Thus, by affixing a proper length to this line of impulse, it was always in his power to reconcile any two shots made at different angles, let them differ as widely as we please to suppose. But this he could not have done with three shots; nor indeed doth he ever tell us the event of his experiments when three ranges were tried at one time.

When Sir Isaac Newton's Principia was published, he particularly considered the resistance of the air to projectiles which moved with small velocities; but as he never had an opportunity of making experiments down by Newton, on those which move with such prodigious swiftness, he did not imagine that a difference in velocity could make such differences in the resistance as are now found to take place. Sir Isaac found, that, in small velocities, the resistance was increased in the duplicate proportion of the swiftness with which the body moved; that is, a body moving with twice the velocity of another of equal magnitude, would meet with four times as much resistance as the first; with thrice the velocity it would meet with nine times the resistance, &c.—This principle itself is now found to be erroneous with regard to military projectiles; though, if it had been properly attended to, the resistance of the air might even from thence have been reckoned much more considerable than was commonly done. So far, however, were those who treated this subject scientifically, from giving a proper allowance for the resistance of the atmosphere, that their theories 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. All the rest of the learned acquiesced in the justness of Galileo's doctrine, and very erroneous calculations concerning the ranges of cannon were accordingly given. Nor was any notice taken of these errors till the year 1716. At that time Mr Reffons, a French officer of artillery, distinguished by the number of sieges at which he had served, by his high military rank, and by his abilities in his profession, gave in a memoir to the Royal Academy, of which he was a member, 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 agreeably to these calculations, he had never been able to establish any solid foundation upon them."

From the history of the academy, it doth not appear that the sentiments of Mr Reffons were at any time controverted, or any reason offered for the failure of the theory of projectiles when applied to use. Nothing farther, however, was done till the time of Benjamin Robins, who in 1742 published a treatise, intitled, New Principles of Gunnery, in which he hath treated particularly not only of the resistance of the atmosphere, but almost every thing else relating to the flight of military projectiles, and indeed advanced the theory of gunnery much nearer perfection than ever it was before.

The first thing considered by Mr Robins, and which is indeed the foundation of all other particulars relative to gunnery, is the explosive force of gunpowder. This he determined to be owing to an elastic fluid similar to our atmosphere, having its elastic force greatly increased by the heat. "If a red-hot iron (says he) be included in a receiver, and the receiver be exhausted, and gunpowder be then let fall on the iron, the powder will take fire, and the mercurial gage will suddenly descend upon the explosion; and though it immediately ascends again, it will never rise to the height it first stood at, but will continue depressed by a space proportioned to the quantity of powder which was let fall on the iron."—The same production likewise takes place when gunpowder is fired in the air: for if a small quantity of powder is placed in the upper part of a glass tube, the lower part of which is immersed in water, and the fluid be made to rise so near the top, that only a small portion of air is left in that part where the gunpowder is placed; if in this situation the communication of the upper part of the tube with the external air is closed, and the gunpowder fired, which may be easily done by means of a burning-glass, the water will in this experiment descend on the explosion, as the quicksilver did in the last; and will always continue depressed below the place at which it stood before the explosion. The quantity of this depression will be greater if the quantity of powder be increased, or the diameter of the tube be diminished.

"When any considerable quantity of gunpowder is fired in an exhausted receiver, by being let fall on a red-hot iron, the mercurial gage instantly descends upon the explosion, and as suddenly ascends again. After a few vibrations, none of which except the first are of any great extent, it seemingly fixes at a point lower than where it stood before the explosion. But even when the gage has acquired this point of apparent rest, it still continues rising for a considerable time, although by such imperceptible degrees, that it can only be discovered by comparing its place at distant intervals: however, it will not always continue to ascend; but will rise slower and slower, till at last it will be absolutely fixed at a point lower than where the mercury stood before the explosion. The same circumstances nearly happen, when powder is fired in the upper part of an unexhausted tube, whose lower part is immersed in water.

"That the elasticity or pressure of the fluid produced by the firing of gunpowder is, ceteris paribus, directly as its density, may be proved from hence, that if in the same receiver a double quantity of powder be let fall, the mercury will subside twice as much as in the firing of a single quantity. Also the descents of the mercury, when equal quantities of powder are fired in different receivers, are reciprocally as the capacities of those receivers, and consequently as the density of produced fluid in each. But as, in the usual method of trying this experiment, the quantities of powder are so very small that it is difficult to ascertain these proportions with the requisite degree of exactness, I took a large receiver containing about 520 inches, and letting fall at once on the red-hot iron one drachm or the sixteenth part of an ounce avoirdupois of powder, the receiver being first nearly exhausted; the mercury, after the explosion, was subside two inches exactly, and all the powder had taken fire. Then heating the iron a second time, and exhausting the receiver as before, two drachms were let down at once, which sunk the mercury three inches and three quarters; and a small part of the powder had fallen beside the iron, which (the bottom of the receiver being wet) did not fire, and the quantity which thus escaped did appear to be nearly sufficient, had it fallen on the iron, to have sunk the mercury a quarter of an inch more; in which case the two descents, viz. two inches and four inches, would have been accurately in the proportion of the respective quantities of powder; from which proportion, as it was, they very little varied.

"As different kinds of gunpowder produce different quantities of this fluid, in proportion to their different degrees of goodness, before any definite determination of this kind can take place, it is necessary to ascertain the particular species of powder that is proposed to be used. (Here Mr Robins determines in all his experiments to make use of government-powder, as consisting of a certain and invariable proportion of materials, and therefore preferable to such kinds as are made according to the fancy of private persons.)

"This being settled, we must further premise these two principles: 1. That the elasticity of this fluid increases by heat and diminishes by cold, in the same manner as that of the air; 2. That the density of this fluid, and consequently its weight, is the same with the weight of an equal bulk of air, having the same elasticity and the same temperature. Now from the last experiment it appears, that ⅓ of an ounce avoirdupois or about 27 grains Troy of powder, sunk the gage, on its explosion, two inches; and the mercury in the barometer standing at near 30 inches, ⅔ths of an ounce avoirdupois, or 410 grains Troy, would have filled the receiver with a fluid whose elasticity would have been equal to the whole pressure of the atmosphere, or the same with the elasticity of the air we breathe; and the content of the receiver being about 520 cubic inches, it follows, that ⅔ths of an ounce of powder will produce 520 cubic inches of a fluid possessing the same degree of elasticity with the common air; whence an ounce of powder will produce near 575 cubic inches of such a fluid.

"But in order to ascertain the density of this fluid, we must consider what part of its elasticity, at the time of this determination, was owing to the heat it received from the included hot-iron and the warm receiver. Now the general heat of the receiver being manifestly less than that of boiling water, which is known to increase the elasticity of the air to somewhat more than ⅔ of its augmented quantity; I collect from hence and other circumstances, that the augmentation of elasticity from this cause was about ⅓ of the whole: that is, if the fluid arising from the explosion had been reduced to the temperature of the external air, the descent of the the mercurial gage, instead of two inches, would have been only \( \frac{1}{4} \) inch; whence 575, reduced in the proportion of five to four, becomes 460; and this last number represents the cubic inches of an elastic fluid equal in density and elasticity with common air, which are produced from the explosion of 1 ounce avoirdupois of gunpowder; the weight of which quantity of fluid, according to the usual estimation of the weight of air, is 131 grams; whence the weight of this fluid is \( \frac{4}{3} \times \frac{3}{4} = \frac{3}{4} \) or \( \frac{3}{4} \) nearly of the weight of the generating powder. The ratio of the bulk of gunpowder to the bulk of this fluid may be determined from considering that 17 drams avoirdupois of powder fill two cubic inches, if the powder be well hooked together; therefore, augmenting the number last found in the proportion of 16 to 17, the resulting term 488\( \frac{1}{2} \) is the number of cubic inches of an elastic fluid, equal in density with the air produced from two cubic inches of powder: whence the ratio of the respective bulk of the powder, and of the fluid produced from it, is in round numbers as 1 to 244.

This calculation was afterwards justified by experiments.

"If this fluid, instead of expanding when the powder was fired, had been confined in the same space which the powder filled before the explosion; then it would have had, in that confined state, a degree of elasticity 244 times greater than that of common air; and this independent of the great augmentation this elasticity would receive from the action of the fire in that instant.

"Hence, then, we are certain, that any quantity of powder, fired in a confined space, which it adequately fills, exerts, at the instant of its explosion, against the sides of the vessel containing it, and the bodies it impels before it, a force at least 244 times greater than the elasticity of the common air; or, which is the same thing, than the pressure of the atmosphere; and this without considering the great addition which this force will receive from the violent degree of heat with which it is affected at that time.

"To determine how far the elasticity of air is augmented when heated to the extreme degree of red-hot iron, I took a piece of a mulecot barrel about six inches in length, and ordered one end to be closed up entirely; but the other end was drawn out conically, and finished in an aperture of about \( \frac{1}{8} \) of an inch in diameter. The tube thus fitted, was heated to the extremity of a red heat in a smith's forge; and was then immersed with its aperture downwards in a bucket of water, and kept there till it was cool; after which it was taken out carefully, and the water which had entered it in cooling was exactly weighed. The heat given to the tube at each time, was the beginning of what workmen call a white heat; and to prevent the rushing in of the aqueous vapour at the immersion, which would otherwise drive out great part of the air, and render the experiment fallacious, I had an iron wire filed tapering, so as to fit the aperture of the tube, and with this I always stopped it up before it was taken from the fire, letting the wire remain in till the whole was cool, when, removing it, the due quantity of water would enter. The weight of the water thus taken in at three different trials was 610 grains, 595 grains, and 600 grains, respectively. The content of the whole cavity of the tube was 796 grains of water; whence the spaces remaining unfilled in these three experiments were 186, 201, and 196 grains respectively. These spaces undoubtedly contained all the air which, when the tube was red-hot, extended through its whole concavity; consequently the elasticity of the air, when heated to the extreme heat of red-hot iron, was to the elasticity of the same air, when reduced to the temperature of the ambient atmosphere, as the whole capacity of the tube to the respective spaces taken up by the cooled air; that is, as 796 to 186, 201, 196; or, taking the medium of these three trials, as 796 to 194\( \frac{1}{2} \).

"As air and this fluid appear to be equally affected by heat and cold, and consequently have their elasticities equally augmented by the addition of equal degrees of heat to each; if we suppose the heat with which the flame of fired powder is endowed to be the same with that of the extreme heat of red-hot iron, then the elasticity of the generated fluid will be greater at the time of the explosion than afterwards, when it is reduced to the temperature of the ambient air, in the ratio of 796 to 194\( \frac{1}{2} \) nearly. It being allowed then, (which surely is very reasonable), that the flame of gunpowder is not less hot than red-hot iron, and the elasticity of the air, and consequently of the fluid generated by the explosion, being augmented in the extremity of this heat in the ratio of 194\( \frac{1}{2} \) to 796, it follows, that if 244 be augmented in this ratio, the resulting number, which is 999\( \frac{1}{2} \), will determine how many times the elasticity of the flame of fired powder exceeds the elasticity of common air, supposing it to be confined in the same space which the powder filled before it was fired.—Hence then the absolute quantity of the pressure exerted by gunpowder at the moment of its explosion may be assigned; for, since the fluid then generated has an elasticity of 999\( \frac{1}{2} \), or in round numbers 1000 times greater than that of the atmosphere, and since common air by its elasticity exerts a pressure on any given surface equal to the weight of the incumbent atmosphere with which it is in equilibrium, the pressure exerted by fired powder before it dilated itself is 1000 times greater than the pressure of the atmosphere; and consequently the quantity of this force, on a surface of an inch square, amounts to above six ton weight; which force, however, diminishes as the fluid dilates itself.

"But though we have here supposed that the heat of gunpowder, when fired in any considerable quantity, is the same with iron heated to the extremity of red heat, or to the beginning of a white heat, yet it cannot be doubted but that the fire produced in the explosion is somewhat varied (like all other fires) by a greater or lesser quantity of fuel; and it may be presumed, that, according to the quantity of powder fired together, the flame may have all the different degrees, from a languid red heat to that sufficient for the vitrification of metals. But as the quantity of powder requisite for the production of this last mentioned heat, is certainly greater than what is ever fired together for any military purpose, we cannot be far from our scope, if we suppose the heat of such quantities as are usually fired to be nearly the same with that of red-hot iron; allowing a gradual augmentation to this heat in larger quantities, and diminishing it when the quantities are very small."

Having Having thus determined the force of the gunpowder, Mr Robins next proceeds to determine the velocity with which the ball is discharged. The solution of this problem depends on the two following principles. 1. That the action of the powder on the bullet ceases as soon as the bullet is got out of the piece. 2. That all the powder of the charge is fired and converted into elastic fluid before the bullet is sensibly moved from its place.

"The first of these (says Mr Robins) will appear manifest when it is considered how suddenly the flame will extend itself on every side, by its own elasticity, when it is once got out of the mouth of the piece; for by this means its force will then be dissipated, and the bullet no longer sensibly affected by it.

"The second principle is indeed less obvious, being contrary to the general opinion of almost all writers on this subject. It might, however, be sufficient for the proof of this position, to observe the prodigious compression of the flame in the chamber of the piece. Those who attend to this circumstance, and to the easy passage of the flame through the intervals of the grains, may soon satisfy themselves, that no one grain contained in that chamber can continue for any time unflamed, when thus surrounded and pressed by such an active fire. However, not to rely on mere speculation in a matter of so much consequence, I considered, that if part only of the powder is fired, and that successively; then by laying a greater weight before the charge (suppose two or three bullets instead of one), a greater quantity of powder would necessarily be fired, since a heavier weight would be a longer time in passing through the barrel. Whence it should follow, that two or three bullets would be impelled by a much greater force than one only. But the contrary to this appears by experiment; for firing one, two, and three bullets laid contiguous to each other with the same charge respectively, I have found that their velocities were not much different from the reciprocal of their subduplicate quantities of matter; that is, if a given charge would communicate to one bullet a velocity of 1700 feet in a second, the same charge would communicate to two bullets a velocity from 1250 to 1300 feet in a second, and to three bullets a velocity from 1050 to 1110 feet in the same time. From hence it appears, that, whether a piece is loaded with a greater or less weight of bullets, the action is nearly the same; since all mathematicians know, that if bodies containing different quantities of matter are successively impelled through the same space by the same power acting with a determined force at each point of that space; then the velocities given to these different bodies will be reciprocally in the subduplicate ratio of their quantities of matter. The excess of the velocities of the two and three bullets above what they ought to have been by this rule (which are that of 1200 and 980 feet in a second), undoubtedly arises from the flame, which, escaping by the side of the first bullet, acts on the surface of the second and third.

"Now, this excess has in many experiments been imperceptible, and the velocities have been reciprocally in the subduplicate ratios of the number of bullets, to sufficient exactness; and where this error has been greater, it has never arisen to an eighth part of the whole: but if the common opinion was true, that a small part only of the pow derfires at first, and other parts of it successively as the bullet passes through the barrel, and that a considerable part of it is often blown out of the piece without firing at all; then the velocity which three bullets received from the explosion ought to have been much greater than we have found it to be.—But the truth of this second postulate more fully appears from those experiments, by which it is shown, that the velocities of bullets may be ascertained to the same exactness when they are acted on through a barrel of four inches in length only, as when they are discharged from one of four feet.

"With respect to the grains of powder which are often blown out unfired, and which are always urged as a proof of the gradual firing of the charge, I believe Diego Uffano, a person of great experience in the art of gunnery, has given the true reason for this accident; which is, that some small part of the charge is often not rammed up with the rest, but is left in the piece before the wad, and is by this means expelled by the blast of air before the fire can reach it. I must add, that, in the charging of cannon and small arms, especially after the first time, this is scarcely to be avoided by any method I have yet seen practised. Perhaps, too, there may be some few grains in the best powder, of such an heterogeneous composition as to be less susceptible of firing; which, I think, I have myself observed; and these, though they are surrounded by the flame, may be driven out unfired.

"These postulates being now allowed to be just, let Demonstra-

AB represent the axis of any piece of artillery, A the point of the breech, and B the muzzle; DC the diameter of its red powder bore, and DEGC a part of its cavity filled with powder on the ball. Suppose the ball that is to be impelled to lie Plate with its hinder surface at the line GE; then the pressure exerted at the explosion on the circle of which GE is the diameter, or, which is the same thing, the pressure exerted in the direction FB on the surface of the ball, is easily known from the known dimensions of that circle. Draw any line FH perpendicular to FB, and AI parallel to FH; and through the point H to the asymptotes IA and AB, describe the hyperbola KHNO; then, if FH represents the force impelling the ball at the point F, the force impelling the ball at any other point as at M, will be represented by the line MN, the ordinate to the hyperbola at that point. For when the fluid impelling the body along has dilated itself to M, its density will be then to its original density in the space DEGC reciprocally as the spaces through which it is extended; that is, as FA to MA; or as MN to FH; but it has been shown, that the impelling force or elasticity of this fluid is directly as its density; therefore, if FH represents the force at the point F, MN will represent the like force at the point M.

"Since the absolute quantity of the force impelling the ball at the point F is known, and the weight of the ball is also known, the proportion between the force with which the ball is impelled and its own gravity is known. In this proportion take FH to FL, and draw LP parallel to FB; then, MN the ordinate to the hyperbola in any point will be to its part MR, cut off by the line LP, as the impelling force of the powder in that point M to the gravity of the ball; and con- Theory. consequently the line L.P will determine a line proportional to the uniform force of gravity in every point; whilst the hyperbola H.N.Q determines in like manner such ordinates as are proportional to the impelling force of the powder in every point; whence by the 39th Prop. of lib. I. of Sir Isaac Newton's Principia, the areas F.L.P.B and F.H.Q.B are in the duplicate proportion of the velocities which the ball would acquire when acted upon by its own gravity through the space F.B, and when impelled through the same space by the force of the powder. But since the ratio of A.F to A.B and the ratio of F.H to F.L are known, the ratio of the area F.L.P.B to the area F.H.Q.B is known; and thence its subduplicate. And since the line F.B is given in magnitude, the velocity which a heavy body would acquire when impelled through this line by its own gravity is known; being no other than the velocity it would acquire by falling through a space equal to that line: find then another velocity to which this last mentioned velocity bears the given ratio of the subduplicate of the area F.L.P.B to the area F.H.Q.B; and this velocity thus found is the velocity the ball will acquire when impelled through the space F.B by the action of the inflamed powder.

"Now to give an example of this: Let us suppose A.B, the length of the cylinder, to be 45 inches, its diameter D.C., or rather the diameter of the ball, to be 2/3ths of an inch; and A.F, the extent of the powder, to be 2/3ths inches; to determine the velocity which will be communicated to a leaden bullet by the explosion, supposing the bullet to be laid at first with its surface contiguous to the powder.

"By the theory we have laid down, it appears, that at the first instant of the explosion the flame will exert, on the bullet lying close to it, a force 1000 times greater than the pressure of the atmosphere. The medium pressure of the atmosphere is reckoned equal to a column of water 33 feet in height; whence, lead being to water as 11,345 to 1, this pressure will be equal to that of a column of lead 349 inches in height. Multiplying this by 1000, therefore, a column of lead 34900 inches (upwards of half a mile) in height would produce a pressure on the bullet equal to what is exerted by the powder in the first instant of the explosion; and the leaden ball being 2/3ths of an inch in diameter, and consequently equal to a cylinder of lead of the same base half an inch in height, the pressure at first acting on it will be equal to 34900 x 2, or 69800 times its weight: whence F.L to F.H as 1 to 69800; and F.B to F.A as 45 - 2/3; or 42 1/3 to 2/3; that is, as 339 to 21; whence the rectangle F.L.P.B is to the rectangle A.F.H.S as 339 to 21 x 69800, that is, as 1 to 4324.—And from the known application of the logarithms to the mensuration of the hyperbolic spaces it follows, that the rectangle A.F.H.S is to the area F.H.Q.B as 4324, &c. is to the tabular logarithm of \(\frac{A.B}{A.F}\) (where A.B represents the length of the barrel, and A.F the length of the cavity left behind the bullet); also directly as the part of that cavity filled with powder; and inversely, as the diameter of the bore, or rather of the bullet, likewise directly as A.F, the height of the cavity left behind the bullet. Consequently the velocity being computed as above, for a bullet of a determined diameter, placed in a piece of a given length, and impelled by a given quantity of powder, occupying a given cavity behind that bullet; it follows, that by means of these ratios, the velocity of any other bullet may be thence deduced; the necessary circumstances of its position, quantity of powder, &c. being given. Where note, That in the instance of this supposition, we have supposed the diameter of the ball to be 2/3ths of an inch; whence the diameter of the bore will be something more, and the quantity of powder contained in the space D.E.G.C will amount exactly to 12 pennyweight, a small wad of tow included.

"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 discovered. The only methods hitherto practised for this purpose, have been either by observing the time of the flight of a shot through a given space, or by measuring the range of a shot at a given elevation; and thence computing, on the parabolic hypothesis, Theory. what degree of 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 to fallacious, by reason of the resistance of the atmosphere (to which inequality the first is also liable), that the velocities thus assigned may not perhaps be the tenth part of the actual velocities sought.

"The simplest method of determining this velocity is by means of the instrument represented fig. 2, where ABCD represents the body of the machine composed of the three poles B, C, D, spreading at bottom, and joining together at the top A; being the same with what is vulgarly used in lifting and weighing very heavy bodies, and is called by workmen the triangles. On two of these poles, towards their tops, are screwed on the sockets RS; and on these sockets the pendulum EFGHIK is hung by means of its cross-piece EF, which becomes its axis of suspension, and on which it must be made to vibrate with great freedom. The body of this pendulum is made of iron, having a broad part at bottom, and its lower part is covered with a thick piece of wood GKIH, which is fastened to the iron by screws. Something lower than the bottom of the pendulum there is a brace OP, joining the two poles to which the pendulum is suspended; and to this brace there is fastened a contrivance MNU, made with two edges of steel, bearing on each other in the line UN, something in the manner of a drawing-pen; the strength with which these edges press on each other being diminished or increased at pleasure by means of a screw Z going through the upper piece. There is fastened to the bottom of the pendulum a narrow ribbon LN, which passes between these steel edges, and which afterwards, by means of an opening cut in the lower piece of steel, hangs loosely down, as at W.

"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.

"Now the extent of the vibration made by the pendulum after the blow, may be measured to great accuracy by the ribbon LN. For let the pressure of the edges UN on the ribbon be so regulated by the screw Z, that the motion of the ribbon between them may be free and easy, though with some minute resistance; then settling the pendulum at rest, let the part LN between the pendulum and the edges be drawn tight, but not strained, and fix a pin in that part of the ribbon which is then contiguous to the edges; let now a ball impinge on the pendulum; then the pendulum swinging back will draw out the ribbon to the just extent of its vibration, which will consequently be determined by the interval on the ribbon between the edges UN and the place of the pin.

"The weight of the whole pendulum, wood and all, was 56 lb. 3 oz. Its centre of gravity was 52 inches distant from its axis of suspension, and 200 of its small swings were performed in the time of 253 seconds; whence its centre of oscillation (determined from hence) is 62½ inches distant from that axis. The centre of the piece of wood GKIH is distant from the same axis 66 inches.

"In the compound ratio of 66 to 62½, and 66 to 52, take the quantity of matter of the pendulum to a 4th quantity, which will be 42 lb. ½ oz. Now geometers will know, that if the blow be struck on the centre of the piece of wood GKIH, the pendulum will reflect to the stroke in the same manner as if this last quantity of matter only (42 lb. ½ oz.) was concentrated in that point, and the rest of the pendulum was taken away; whence, supposing the weight of the bullet impinging in that point to be the ¼th of a pound, or the ¼th of this quantity of matter nearly, the velocity of the point of oscillation after the stroke will, by the laws observed in the congress of such bodies as rebound not from each other, be the ¼th of the velocity the bullet moved with before the stroke; whence the velocity of this point of oscillation after the stroke being ascertained, that multiplied by 505 will give the velocity with which the ball impinged.

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

"For instance, the chord of the arch, described by the ascent of the pendulum after the stroke measured on the ribbon, has been sometimes 17½ inches; the distance of the ribbon from the axis of suspension is 71½ inches; whence reducing 17½ in the ratio of 71½ to 66, the resulting number, which is nearly 16 inches, will be the chord of the arch through which the centre of the board GKIH ascended after the stroke; now the verified fine of the arch, whose chord is 16 inches, and its radius 66, is 1.93939; and the velocity which would carry a body to this height, or, which is the same thing, the velocity which a body would acquire by descending through this space, is nearly that of 3½ feet in 1". To determine then the velocity with which the bullet impinged on the centre of the wood, when the chord of the arch described by the ascent of the pendulum, in consequence of the blow, was \( \frac{1}{4} \) inches measured on the ribbon, no more is necessary than to multiply \( \frac{3}{4} \) by 505, and the resulting number 164.1 will be the feet which the bullet would describe in \( \frac{1}{4} \), if it moved with the velocity it had at the moment of its percussion; for the velocity of the point of the pendulum, on which the bullet struck, we have just now determined to be that of \( \frac{3}{4} \) feet in \( \frac{1}{4} \); and we have before shown, that this is the \( \frac{3}{4} \)th of the velocity of the bullet. If then a bullet weighing \( \frac{1}{4} \)th of a pound strikes the pendulum in the centre of the wood GKH, and the ribbon be drawn out \( \frac{1}{4} \)th inches by the blow; the velocity of the bullet is that of 164.1 feet in \( \frac{1}{4} \).

And since the length the ribbon is drawn is always nearly the chord of the arch described by the ascent, (it being placed so as to differ insensibly from those chords which most frequently occur), and these chords are known to be in the proportion of the velocities of the pendulum acquired from the stroke; it follows, that the proportion between the lengths of ribbon drawn out at different times, will be the same with that of the velocities of the impinging bullets; and consequently, by the proportion of these lengths of ribbon to \( \frac{1}{4} \), the proportion of the velocity with which the bullets impinge, to the known velocity of 164.1 feet in \( \frac{1}{4} \), will be determined.

Hence then is shown in general how the velocities of bullets of all kinds may be found out by means of this instrument; but that those who may be disposed to try these experiments may not have unforeseen difficulties to struggle with, we shall here subjoin a few observations, which it will be necessary for them to attend to, both to secure success to their trials and safety to their persons.

And first, that they may not conceive the piece of wood GKH to be an unnecessary part of the machine, we must inform them, that if a bullet impelled by a full charge of powder should strike directly on the iron, the bullet would be beaten into shivers by the stroke, and these shivers will rebound back with such violence, as to bury themselves in any wood they chance to light on, as I have found by hazardous experience; and besides the danger, the pendulum will not in this instance ascertain the velocity of the bullet, because the velocity with which the parts of it rebound is unknown.

The weight of the pendulum, and the thickness of the wood, must be in some measure proportioned to the size of the bullets which are used. A pendulum of the weight here described will do very well for all bullets under three or four ounces, if the thickness of the board be increased to seven or eight inches for the heaviest bullets; beech is the toughest and properest wood for this purpose.

It is hazardous standing on the side of the pendulum, unless the board be so thick, that the greatest part of the bullet's force is lost before it comes at the iron; for if it strikes the iron with violence, the shivers of lead, which cannot return back through the wood, will force themselves out between the wood and iron, and will fly to a considerable distance.

As there is no effectual way of fastening the wood to the iron but by screws, the heads of which must come through the board; the bullets will sometimes light on those screws, from whence the shivers will disperse themselves on every side.

When in these experiments so small a quantity of powder is used, as will not give to the bullet a velocity of more than 400 or 500 feet in \( \frac{1}{4} \); the bullet will not stick in the wood, but will rebound from it entirely, and (if the wood be of a very hard texture) with a very considerable velocity. Indeed I have never examined any of the bullets which have thus rebounded, but I have found them indented by the bodies they have struck against in their rebound.

To avoid these dangers, to the brawling of which in philosophical researches no honour is annexed; it will be convenient to fix whatsoever barrel is used, on a strong heavy carriage, and to fire it with a little flow match. Let the barrel too be very well fortified in all its length; for no barrel (I speak of musket barrels) forged with the usual dimensions will bear many of the experiments without bursting. The barrel I have most relied on, and which I procured to be made on purpose, is nearly as thick at the muzzle as at the breech; that is, it has in each place nearly the diameter of its bore in thickness of metal.

The powder used in these experiments should be exactly weighed; and that no part of it be scattered in the barrel, the piece must be charged with a ladle in the same manner as is practised with cannon; the wad should be of tow, of the same weight each time, and no more than is just necessary to confine the powder in its proper place: the length of the cavity left behind the ball should be determined each time with exactness; for the increasing or diminishing that space will vary the velocity of the shot, although the bullet and quantity of powder be not changed. The distance of the mouth of the piece from the pendulum ought to be such, that the impulse of the flame may not act on the pendulum; this will be prevented in a common barrel charged with \( \frac{1}{4} \) an ounce of powder, if it be at the distance of 16 or 18 feet: in larger charges the impulse is sensible farther off; I have found it to extend to above 25 feet; however, between 25 and 18 feet is the distance I have usually chosen.

With this instrument, or others similar to it, Mr Account Robins made a great number of experiments on bar-ber's-powder. He hath given us the results of 61 of these; and having compared the actual velocities with the computed ones, his theory appears to have come as near the truth as could well be expected. In seven of the experiments there was a perfect coincidence; the charges of powder being six or twelve pennyweights; the barrels 45, 24, 312, and 7.66 inches in length. The diameter of the first (marked A) was \( \frac{1}{4} \)ths of an inch; of the second (B) was the same; and of D, \( \frac{1}{4} \) of an inch. In the rest of the experiments, another barrel (C) was used, whose length was 12.375 inches, and the diameter of its bore \( \frac{1}{4} \)th inches.—In 14 more of the experiments, the difference between the length of the chord of the pendulum's arch shown by the theory and the actual experiment was \( \frac{1}{4} \)th of an inch over or under. This showed an error in the theory varying according to the different lengths of the chord from \( \frac{1}{4} \) to \( \frac{1}{4} \) of the whole; the charges of powder were... were the same as in the last.—In 16 other experiments the error was \( \frac{3}{5} \)ths of an inch, varying from \( \frac{1}{5} \) to \( \frac{2}{5} \) of the whole; the charges of powder were 6, 8, 9, or 12 pennyweights.—In seven other experiments, the error was \( \frac{1}{5} \)ths of an inch, varying from \( \frac{1}{5} \) to \( \frac{2}{5} \) of the whole; the charges of powder six or twelve pennyweights. In eight experiments, the difference was \( \frac{1}{5} \)ths of an inch, indicating an error from \( \frac{1}{5} \) to \( \frac{2}{5} \) of the whole; the charges being 6, 9, 12, and 24 pennyweights of powder. In three experiments, the error was \( \frac{1}{5} \)ths, varying from \( \frac{1}{5} \)th to \( \frac{2}{5} \)th of the whole; the charges 8 and 12 pennyweights of powder. In two experiments the error was \( \frac{1}{5} \)ths, in one case amounting to something less than \( \frac{1}{5} \)th, in the other to \( \frac{2}{5} \)th of the whole; the charges 12 and 36 pennyweights of powder. By one experiment the error was seven, and by another eight, tenths; the first amounting to \( \frac{1}{5} \)th nearly, the latter to almost \( \frac{2}{5} \)th of the whole; the charges of powder 6 or 12 pennyweights. The last error, however, Mr Robins ascribes to the wind. The two remaining experiments varied from theory by 1.3 inches, somewhat more than \( \frac{1}{5} \)th of the whole; the charges of powder were 12 pennyweights in each; and Mr Robins ascribes the error to the dampness of the powder. In another case, he ascribes an error of \( \frac{1}{5} \)ths to the blast of the powder on the pendulum.

From these experiments Mr Robins deduces the following conclusions. "The variety of these experiments, and the accuracy with which they correspond to the theory, leave us no room to doubt of its certainty."—This theory, as here established, supposes, that, in the firing of gunpowder, about \( \frac{1}{5} \)ths of its substance is converted by the sudden inflammation into a permanently elastic fluid, whose elasticity, in proportion to its heat and density, is the same with that of common air in the like circumstances; it farther supposes, that all the force exerted by gunpowder in its most violent operations, is no more than the action of the elasticity of the fluid thus generated; and these principles enable us to determine the velocities of bullets impelled from fire-arms of all kinds; and are fully sufficient for all purposes where the force of gunpowder is to be estimated.

"From this theory many deductions may be made of the greatest consequence to the practical part of gunnery. From hence the thickness of a piece, which will enable it to confine, without bursting, any given charge of powder, is easily determined, since the effort of the powder is known. From hence appears the inconclusiveness of what some modern authors have advanced, relating to the advantages of particular forms of chambers for mortars and cannon; for all their laboured speculations on this head are evidently founded on very erroneous opinions about the action of fired powder. From this theory too we are taught the necessity of leaving the same space behind the bullet when we would, by the same quantity of powder, communicate to it an equal degree of velocity; since, on the principles already laid down, it follows, that the same powder has a greater or less degree of elasticity, according to the different spaces it occupies. The method which I have always practised for this purpose has been by marking the rammer; and this is a maxim which ought not to be dispensed with when cannon are fired at an elevation, particularly in those called by the French batteries à ricochet.

"From the continued action of the powder, and its manner of expanding described in this theory, and the length and weight of the piece, one of the most essential circumstances in the well directing of artillery may be easily ascertained. All practitioners are agreed, that no shot can be depended on, unless the piece be placed on a solid platform: for if the platform shakes with the first impulse of the powder, it is impossible but the piece must also shake; which will alter its direction, and render the shot uncertain. To prevent this accident, the platform is usually made extremely firm to a considerable depth backwards; so that the piece is not only well supported in the beginning of its motion, but likewise through a great part of its recoil. However, it is sufficiently obvious, that when the bullet is separated from the piece, it can be no longer affected by the trembling of the piece or platform; and, by a very easy computation, it will be found, that the bullet will be out of the piece before the latter hath recoiled half an inch: whence, if the platform be sufficiently solid at the beginning of the recoil, the remaining part of it may be much lighter; and hence a more compendious method of constructing platforms may be found out.

"From this theory also it appears how greatly these authors have been mistaken, who have attributed the force of gunpowder, or at least a considerable part of it, to the action of the air contained either in the powder or between the intervals of the grains; for they have supposed that air to exist in its natural elastic state, and to receive all its addition of force from the heat of the explosion. But from what hath been already delivered concerning the increase of the air's elasticity by heat, we may conclude that the heat of the explosion cannot augment this elasticity to five times its common quantity; consequently the force arising from this cause only cannot amount to more than the 200th part of the real force exerted on the occasion.

"If the whole substance of the powder was converted into an elastic fluid at the instant of the explosion, then from the known elasticity of this fluid assigned by our theory, and its known density, we could easily determine the velocity with which it would begin to expand, and could thence trace out its future augmentations in its progress through the barrel: but as we have shown that the elastic fluid, in which the activity of the gunpowder consists, is only \( \frac{1}{5} \)ths of the substance of the powder, the remaining \( \frac{4}{5} \)ths will, in the explosion, be mixed with the elastic part, and will by its weight retard the activity of the explosion; and yet they will not be so completely united as to move with one common motion; but the unelastic part will be less accelerated than the rest, and some will not even be carried out of the barrel, as appears by the considerable quantity of unctuous matter which adheres to the inside of all fire-arms after they have been used.—These inequalities in the expansive motion of the flame oblige us to recur to experiments for its accurate determination.

"The experiments made use of for this purpose were of two kinds. The first was made by charging the barrel A with 12 pennyweights of powder, and a... small wad of tow only; and then placing its mouth 19 inches from the centre of the pendulum. On firing it in this situation, the impulse of the flame made it ascend through an arch whose chord was 13.7 inches; whence, if the whole substance of the powder was supposed to strike against the pendulum, and each part to strike with the same velocity, that common velocity must have been at the rate of about 2650 feet in a second.—But as some part of the velocity of the flame was lost in passing through 19 inches of air; I made the remaining experiments in a manner not liable to this inconvenience.

"I fixed the barrel A on the pendulum, so that its axis might be both horizontal and also perpendicular to the plane HK; or, which is the same thing, that it might be in the plane of the pendulum's vibration: the height of the axis of the piece above the centre of the pendulum was six inches; and the weight of the piece, and of the iron that fastened it, &c. was 12½ lb. The barrel in this situation being charged with 12 penny-weights of powder, without either ball or wad, only put together with the rammer; on the discharge the pendulum ascended through an arch whose chord was 10 inches, or reduced to an equivalent blow in the centre of the pendulum, supposing the barrel away, it would be 14.4 inches nearly.—The same experiment being repeated, the chord of the ascending arch was 10.1 inches, which, reduced to the centre, is 14.6 inches.

"To determine what difference of velocity there was in the different parts of the vapour, I loaded the piece again with 12 penny-weights of powder, and rammed it down with a wad of tow, weighing one penny-weight. Now, I conceived that this wad being very light, would presently acquire that velocity with which the elastic part of the fluid would expand itself when uncompressed; and I accordingly found, that the chord of the ascending arch was by this means increased to 12 inches, or at the centre to 17.3; whence, as the medium of the other two experiments is 14.5, the pendulum ascended through an arch 2.8 inches longer, by the additional motion of one penny-weight of matter, moving with the velocity of the swiftest part of the vapour; and consequently the velocity with which this penny-weight of matter moved, was that of about 7000 feet in a second.

"It will perhaps be objected to this determination, that the augmentation of the arch through which the pendulum vibrated in this case was not all of it owing to the quantity of motion given to the wad, but part of it was produced by the confinement of the powder, and the greater quantity thereby fired. But if it were true that a part only of the powder fired when there was no wad, it would not happen that in firing different quantities of powder without a wad the chord would increase and decrease nearly in the ratio of these quantities; which yet I have found it to do: for with nine pennyweights that chord was 7.3 inches, which with 12 pennyweights we have seen was only 10, and 10.1 inches; and even with three pennyweights the chord was two inches; deficient from this proportion by .5 only; for which defect too other valid reasons are to be assigned.

"And there is still a more convincing proof that all the powder is fired, although no wad be placed before the charge, which is, that the part of the recoil arising from the expansion of powder alone, is found to be no greater when it impels a leaden bullet before it, than when the same quantity is fired without any wad to confine it. We have seen that the chord of the arch through which the pendulum rose from the expansive force of the powder alone is 10, or 10.1; and the chord of that arch, when the piece was charged in the customary manner with a bullet and wad, I found to be the first time 22½, and the second 22¾, or at a medium 22.56. Now the impulse of the ball and wad, if they were supposed to strike the pendulum in the same place in which the barrel was suspended, with the velocity they had acquired at the mouth of the piece, would drive it through an arch whose chord would be about 12.3; as is known from the weight of the pendulum, the weight and position of the barrel, and the velocity of the bullet determined by our former experiments; whence, subtracting this number 12.3 from 22.56, the remainder 10.26 is nearly the chord of the arch which the pendulum would have ascended through from the expansion of the powder alone with a bullet laid before it. And this number, 10.26, differs but little from 10.1, which we have above found to be the chord of the ascending arch, when the same quantity of powder expanded itself freely without either bullet or wad before it.

"Again, that this velocity of 7000 feet in a second is not much beyond what the most active part of the flame acquires in expanding, is evinced hence, that in some experiments a ball has been found to be discharged with a velocity of 2400 feet in a second; and yet it appeared not that the action of the powder was at all diminished on account of this immense velocity: consequently the degree of swiftness with which, in this instance, the powder followed the ball without losing any part of its pressure, must have been much short of what the powder alone would have expanded with, had not the ball been there.

"From these determinations may be deduced the force of petards; since their action depends entirely on the impulse of the flame; and it appears that a quantity of powder properly disposed in such a machine, may produce as violent an effort as a bullet of twice its weight, moving with a velocity of 1400 or 1500 feet in a second.

"In many of the experiments already recited, the ball was not laid immediately contiguous to the powder, but at a small distance, amounting, at the nearest, only to an inch and a half. In these cases the theory agreed very well with the experiments. But laid at a distance from the powder, suppose at 12, 18, or 24 inches, we cannot then apply to this ball the same principles which may be applied to those laid in contact, or nearly so, with the powder; for when the surface of the fired powder is not confined by a heavy body, the flame dilates itself with a velocity far exceeding that which it can communicate to a bullet by its continued pressure: consequently, as at the distance of 12, 18, or 24 inches, the powder will have acquired a considerable degree of this velocity of expansion, the first motion of the ball will not be produced by the continued pressure of the powder, but by the actual percussion of the flame." Theory: flame; and it will therefore begin to move with a quantity of motion proportioned to the quantity of this flame, and the velocities of its respective parts.

"From hence then it follows, that the velocity of the bullet, laid at a considerable distance before the charge, ought to be greater than what would be communicated to it by the pressure of the powder acting in the manner already mentioned: and this deduction from our theory we have confirmed by manifold experience; by which we have found, that a ball laid in the barrel A, with its hinder part 11\(\frac{1}{2}\) inches from its breech, and impelled by 12 pennyweights of powder, has acquired a velocity of about 1400 feet in a second; when, if it had been acted on by the pressure of the flame only, it would not have acquired a velocity of 1200 feet in a second. The same we have found to hold true in all other greater distances (and also in lesser, though not in the same degree), and in all quantities of powder: and we have likewise found, that these effects nearly correspond with what has been already laid down about the velocity of expansion and the elastic and unelastic parts of the flame.

"From hence too arises another consideration of great consequence in the practice of gunnery; which is, that no bullet should at any time be placed at a considerable distance before the charge, unless the piece is extremely well fortified: for a moderate charge of powder, when it has expanded itself through the vacant space, and reaches the ball, will, by the velocity each part has acquired, accumulate itself behind the ball, and thereby be condensed prodigiously; whence, if the barrel be not extremely firm in that part, it must, by means of this re-inforced elasticity, infallibly burst. The truth of this reasoning I have experienced in an exceeding good Tower-muzzle, forged of very tough iron; for charging it with 12 pennyweights of powder, and placing the ball 16 inches from the breech, on firing it, the part of the barrel just behind the bullet was swelled out to double its diameter like a blown bladder, and two large pieces of two inches long were burst out of it.

"Having seen that the entire motion of a bullet laid at a considerable distance from the charge, is acquired by two different methods in which the powder acts on it; the first being the percussion of the parts of the flame, with the velocity they had respectively acquired by expanding, the second the continued pressure of the flame through the remaining part of the barrel; I endeavoured to separate these different actions, and to retain that only which arose from the continued pressure of the flame. For this purpose I no longer placed the powder at the breech, from whence it would have full scope for its expansion; but I scattered it as uniformly as I could through the whole cavity left behind the bullet; imagining that by this means the progressive velocity of the flame in each part would be prevented by the expansion of the neighbouring parts: and I found, that the ball being laid 11\(\frac{1}{2}\) inches from the breech, its velocity, instead of 1400 feet in a second, which it acquired in the last experiments, was now no more than 1100 feet in the second, which is 100 feet short of what according to the theory should arise from the continued pressure of the powder only.

"The reason of this deficiency was, doubtless, the intense motion of the flame: for the accension of the powder thus distributed through so much larger a space than it could fill, must have produced many reverberations and pulsations of the flame; and from these internal agitations of the fluid, its pressure on the containing surface will (as is the case of all other fluids) be considerably diminished; and in order to avoid this irregularity, in all other experiments I took care to have the powder closely confined in as small a space as possible, even when the bullet lay at some little distance from it.

"With regard to the resistance of the air, which Of the resistance of the air affects all military projectiles, it is necessary to premise, that the greatest part of authors have established it as a certain rule, that while the same body moves in the same medium, it is always resisted in the duplicate proportion of its velocity; that is, if the resisting body move in one part of its track with three times the velocity with which it moved in some other part, then its resistance to the greater velocity will be nine times the resistance to the lesser. If the velocity in one place be four times greater than in another, the resistance of the fluid will be 16 times greater in the first than in the second, &c. This rule, however, though pretty near the truth when the velocities are confined within certain limits, is excessively erroneous when applied to military projectiles, where such resistances often occur as could scarcely be effected, on the commonly received principles, even by a treble augmentation of its density.

"By means of the machine already described, I have it in my power to determine the velocity with which a ball moves in any part of its track, provided I can direct the piece in such a manner as to cause the bullet to impinge on the pendulum placed in that part: and therefore, charging a muzzle-barrel three times successively with a leaden ball \(\frac{1}{4}\) of an inch in diameter, and about half its weight of powder; and taking such precaution in weighing of the powder and placing it, that I was assured, by many previous trials, that the velocity of the ball could not differ by 20 feet in a second from its medium quantity; I fired it against the pendulum placed at 25, 75, and 125 feet distance from the mouth of the piece respectively; and I found that it impinged against the pendulum, in the first case, with a velocity of 1670 feet in a second; in the second case, with a velocity of 1550 feet in a second; and in the third case, with a velocity of 1425 feet in a second: so that, in passing through 50 feet of air, the bullet lost a velocity of 120 or 125 feet in a second; and the time of its passing through that space being about \(\frac{1}{30}\) or \(\frac{1}{30}\) of a second, the medium quantity of resistance must, in these instances, have been about 120 times the weight of the ball; which (as the ball was nearly \(\frac{1}{4}\) of a pound) amounts to about 10 lb. avoirdupoise.

"Now, if a computation be made according to the method laid down for compressed fluids in the 38th proposition of Newton's Principia, supposing the weight of water to that of air as 850 to 1, it will be found, that the resistance to a globe of \(\frac{1}{4}\) of an inch diameter, moving with a velocity of about 1600 feet in a second, will not, on these principles, amount to any more than 4\(\frac{1}{2}\) lb. avoirdupoise; whence, as we know that the rules contained in that proposition are very very accurate with regard to flow motions, we may hence conclude, that the resistance of the air in flow motions is less than that in swift motions, in the ratio of $4\frac{1}{2}$ to 1; a proportion between that of 1 to 2, and 1 to 3.

"Again, I charged the same piece a number of times with equal quantities of powder, and balls of the same weight, taking all possible care to give to every shot an equal velocity; and, firing three times against the pendulum placed only 25 feet from the mouth of the piece, the medium of the velocities with which the ball impinged was nearly that of 1690 feet in a second; then removing the piece 175 feet from the pendulum, I found, taking the medium of five shots, that the velocity with which the ball impinged at this distance was 1300 feet in a second; whence the ball, in passing through 150 feet of air, lost a velocity of about 390 feet in a second; and the resistance computed from these numbers, comes out something more than in the preceding instance, it amounting here to between 11 and 12 pounds avoirdupoise; whence, according to these experiments, the resisting power of the air to swift motions is greater than to flow ones, in a ratio which approaches nearer to that of 3 to 1 than in the preceding experiments.

"Having thus examined the resistance to a velocity of 1700 feet in a second, I next examined the resistance to smaller velocities: and for this purpose, I charged the same barrel with balls of the same diameter, but with less powder, and placing the pendulum at 25 feet distance from the piece, I fired against it five times with an equal charge each time: the medium velocity with which the ball impinged, was that of 1180 feet in a second; then, removing the pendulum to the distance of 250 feet, the medium velocity of five shots, made at this distance, was that of 950 feet in a second; whence the ball, in passing through 225 feet of air, lost a velocity of 230 feet in a second; and as it passed through that interval in about $\frac{3}{4}$ of a second, the resisting force to the middle velocity will come out to be near 33½ times the gravity of the ball, or 2 lb. 10 oz. avoirdupoise. Now, the resisting force to the same velocity, according to the laws observed in slower motions, amounts to $\frac{7}{10}$ of the same quantity; whence, in a velocity of 1065 feet in a second, the resisting power of the air is augmented in no greater a proportion than that of 7 to 11; whereas we have seen in the former experiments, that to still greater degrees of velocity the augmentation approached very near the ratio of one to three.

"But farther, I fired three shots, of the same size and weight with those already mentioned, over a large piece of water; so that their dropping into the water being very discernible, both the distance and time of their flight might be accurately ascertained. Each shot was discharged with a velocity of 400 feet in a second; and I had satisfied myself by many previous trials of the same charge with the pendulum, that I could rely on this velocity to ten feet in a second. The first shot flew 313 yards in four seconds and a quarter, the second flew 319 yards in four seconds, and the third 373 yards in five seconds and a half. According to the theory of resistance established for slow motions, the first shot ought to have spent no more than 3.2 seconds in its flight, the second 3.28, and the third 4 seconds: whence it is evident, that every shot was retarded considerably more than it ought to have been had that theory taken place in its motion; consequently the resisting force of the air is very sensibly increased, even in such a small velocity as that of 400 feet in a second.

"As no large shot are ever projected in practice with velocities exceeding that of 1700 feet in a second, it will be sufficient for the purposes of a practical gunner to determine the resisting force to all lesser velocities; which may be thus exhibited. Let AB be taken to AC, in the ratio of 1700 feet in a second to the given velocity to which the resisting power of the air is required. Continue the line AB to D, so that BD may be to AD, as the resisting power of the air to slow motions is to its resisting power to a velocity of 1700 feet in a second; then shall CD be to AD as the resisting power of the air to slow motions is to its resisting power to the given velocity represented by AC.

"From the computations and experiments already mentioned, it plainly appears, that a leaden ball of $\frac{3}{4}$ of an inch diameter, and weighing nearly 1$\frac{1}{2}$ oz. avoirdupoise, if it be fired from a barrel of 45 inches in length, with half its weight of powder, will issue from that piece with a velocity which, if it were uniformly continued, would carry it near 1700 feet in a second.

"—If, instead of a leaden ball, an iron one, of an equal diameter, was placed in the same situation in the same piece, and was impelled by an equal quantity of powder, the velocity of such an iron-bullet would be greater than that of the leaden one in the subduplicate ratio of the specific gravities of lead and iron; and supposing that ratio to be as three to two, and computing on the principles already laid down, it will appear, that an iron-bullet of 24 lb. weight, shot from a piece of 10 feet in length, with 16 lb. of powder, will acquire from the explosion a velocity which, if uniformly continued, would carry it nearly 1650 feet in a second.

"This is the velocity which, according to our theory, a cannon-ball of 24 lb. weight is discharged with when it is impelled by a full charge of powder; but if, instead of a quantity of powder weighing two-thirds of the ball, we suppose the charge to be only half the weight of it, then its velocity will on the same principles be no more than 1400 feet in a second. The same would be the velocities of every lesser bullet fired with the same proportions of powder, if the lengths of all pieces were constantly in the same ratio with the diameters of their bores; and although, according to the usual dimensions of the smaller pieces of artillery, this proportion does not always hold, yet the difference is not great enough to occasion a very great variation from the velocities here assigned; as will be obvious to any one who shall make a computation thereon. But in these determinations we suppose the windage to be no more than is just sufficient for putting down the bullet easily; whereas in real service, either through negligence or unskillfulness, it often happens, that the diameter of the bore so much exceeds the diameter of the bullet, that great part of the inflamed fluid escapes by its side; whence the velocity of the shot in this case may be considerably less than what we have assigned. However, this perhaps may be compensated by the greater heat which in all probability attends the firing of these large quantities of powder." "From this great velocity of cannon-shot we may clear up the difficulty concerning the point-blank shot which occasioned the invention of Anderson's strange hypothesis†. Here our author was deceived by his not knowing how greatly the primitive velocity of the heaviest shot is diminished in the course of its flight by the resistance of the air. And the received opinion of practical gunners is not more difficult to account for; since, when they agree that every shot flies in a straight line to a certain distance from the piece, which imaginary distance they have called the extent of the point-blank shot, we need only suppose, that, within that distance which they thus determine, the deviation of the path of the shot from a straight line is not very perceptible in their method of pointing. Now, as a shot of 24 lb. fired with two-thirds of its weight of powder, will, at the distance of 500 yards from the piece, be separated from the line of its original direction by an angle of little more than half a degree; those who are acquainted with the inaccurate methods often used in the directing of cannon will easily allow, that so small an aberration may not be attended to by the generality of practitioners, and the path of the shot may consequently be deemed a straight line; especially as other causes of error will often intervene much greater than what arises from the incurvation of this line by gravity.

"We have now determined the velocity of the shot both when fired with two-thirds of its weight and powder, with half its weight of powder respectively; and on this occasion I must remark, that on the principles of our theory, the increasing the charge of powder will increase the velocity of the shot, till the powder arrives at a certain quantity; after which, if the powder be increased, the velocity of the shot will diminish. The quantity producing the greatest velocity, and the proportion between that greatest velocity and the velocity communicated by greater and lesser charges, may be thus assigned. Let AB represent the axis of the piece; draw AC perpendicular to it, and to the asymptotes AC and AB draw any hyperbola LF, and draw BF parallel to AC; find out now the point D, where the rectangle ADEG is equal to the hyperbolic area DEFB; then will AD represent that height of the charge which communicates the greatest velocity to the shot: whence AD being to AB as 1 to 2.71828, as appears from the table of logarithms, from the length of the line AD thus determined, and the diameter of the bore, the quantity of powder contained in this charge is easily known. If instead of this charge, any other filling the cylinder to the height AH be used, draw IH parallel to AC, and through the point H to the same asymptotes AC and AB describe the hyperbola HK; then the greatest velocity will be to the velocity communicated by the charge AH, in the subduplicate proportion of the rectangle AE to the same rectangle diminished by the trilinear space KKE.

"It hath been already shown, that the resistance of the air on the surface of a bullet of \( \frac{3}{4} \) of an inch diameter, moving with a velocity of 1670 feet in a second, amounted to about 10 lb. It hath also been shown, that an iron-bullet weighing 24 lb. if fired with 16 lb. of powder (which is usually esteemed its proper battering charge), acquires a velocity of about 1650 feet in a second, scarcely differing from the other: whence, No 146.

"The surface of this last bullet is more than 54 times greater than the surface of a bullet of \( \frac{3}{4} \) of an inch diameter, and their velocities are nearly the same; it follows, that the resistance on the larger bullet will amount to more than 540 lb. which is near 23 times its own weight.

"The two last propositions are principally aimed against those theorists who have generally agreed in supposing the flight of shot and shells to be nearly in the curve of a parabola. The reason given by those authors for their opinion is the supposed inconsiderable resistance of the air; since, as it is agreed on all sides that the tract of projectiles would be a perfect parabola if there was no resistance, it has from thence been too rashly concluded, that the interruption which the ponderous bodies of shells and bullets would receive from such a rare medium as air would be scarcely sensible, and consequently that their parabolic flight would be hereby scarcely affected.

"Now the prodigious resistance of the air to a bullet of 24 lb. weight, such as we have here established it, sufficiently confutes this reasoning; for how erroneous must that hypothesis be, which neglects as inconsiderable a force amounting to more than 20 times the weight of the moving body?" But here it is necessary to affirm a few particulars, the demonstrations of which, on the commonly received principles, may be seen under the article Projectiles.

"1. If the resistance of the air be so small that the common motion of a projected body is in the curve of a parabola, then the axis of that parabola will be perpendicular to the horizon, and consequently the part of the curve in which the body ascends will be equal and similar to that in which it descends.

"2. If the parabola in which the body moves be terminated on a horizontal plane, then the vertex of the parabola will be equally distant from its two extremities.

"3. Also the moving body will fall on that horizontal plane in the same angle, and with the same velocity with which it was first projected.

"4. If a body be projected in different angles but with the same velocity, then its greatest horizontal range will be when it is projected in an angle of 45° with the horizon.

"5. If the velocity with which the body is projected be known, then this greatest horizontal range may be thus found. Compute, according to the common theory of gravity, what space the projected body ought to fall through to acquire the velocity with which it is projected; then twice that space will be the greatest horizontal range, or the horizontal range when the body is projected in an angle of 45° with the horizon.

"6. The horizontal ranges of a body, when projected with the same velocity at different angles, will be between themselves as the sines of twice the angle in which the line of projection is inclined to the horizon.

"7. If a body is projected in the same angle with the horizon but with different velocities, the horizontal ranges will be in the duplicate proportion of those velocities.

"These postulates which contain the principles of Prodigies the modern art of gunnery are all of them false; for common it theory." it hath been already shown, that a musket-ball of an inch in diameter, fired with half its weight of powder, from a piece 45 inches long, moves with a velocity of near 1700 feet in a second. Now, if this ball flew in the curve of a parabola, its horizontal range at 45° would be found by the fifth postulate to be about 17 miles. But all the practical writers assure us, that this range is really short of half a mile. Diego Ufano assigns to an arquebus, four feet in length, and carrying a leaden ball of 1½ oz. weight (which is very near our dimensions), an horizontal range of 797 common paces, when it is elevated between 40 and 50 degrees, and charged with a quantity of fine powder equal in weight to the ball. Mercurius also tells us, that he found the horizontal range of an arquebus at 45° to be less than 400 fathom, or 800 yards; whence, as either of these ranges are short of half an English mile, it follows, that a musket shot, when fired with a reasonable charge of powder at the elevation of 45°, flies not ¼ part of the distance it ought to do if it moved in a parabola. Nor is this great contraction of the horizontal range to be wondered at, when it is considered that the resistance of this bullet when it first issues from the piece amounts to 120 times its gravity, as hath been experimentally demonstrated, n° 23.

"To prevent objections, our next instance shall be in an iron-bullet of 24 lb. weight, which is the heaviest in common use for land-service. Such a bullet fired from a piece of the common dimensions with its greatest allotment of powder hath a velocity of 1650 feet in a second, as already shown. Now, if the horizontal range of this shot, at 45°, be computed on the parabolic hypothesis by the fifth postulate, it will come out to be about 16 miles, which is between five and six times its real quantity; for the practical writers all agree in making it less than three miles.

"But farther, it is not only when projectiles move with these very great velocities that their flight sensibly varies from the curve of a parabola; the same aberration often takes place in such as move slow enough to have their motion traced out by the eye: for there are few projectiles that can be thus examined, which do not visibly disagree with the first, second, and third postulate; obviously descending thro' a curve, which is shorter and less inclined to the horizon than that in which they ascended. Also the highest point of their flight, or the vertex of the curve, is much nearer the place where they fall to the ground than to that from whence they were at first discharged.

"I have found too by experience, that the fifth, sixth, and seventh postulates are excessively erroneous when applied to the motions of bullets moving with small velocities. A leaden bullet ¾ of an inch in diameter, discharged with a velocity of about 400 feet in a second, and in an angle of 10° 5' with the horizon, ranged on the horizontal plane no more than 428 yards; whereas its greatest horizontal range being found by the fifth postulate to be at least 1700 yards, the range at 10° 5' ought by the fifth postulate to have been 1050 yards; whence, in this experiment, the range was not ¼ of what it must have been had the commonly received theory been true."

From this and other experiments it is clearly proved, that the track described by the flight even of the heaviest shot, is neither a parabola, nor approaching to a parabola, except when they are projected with very small velocities. The nature of the curve really described by them is explained under the article PROJECTILES. But as a specimen of the great complication of that subject, we shall here insert an account of a very extraordinary circumstance which frequently takes place therein.

"As gravity acts perpendicularly to the horizon, it is evident, that if no other power but gravity deflected a projected body from its course, its motion would be constantly performed in a plane perpendicular to the horizon, passing through the line of its original direction: but we have found, that the body in its motion often deviates from this plane, sometimes to the right hand and at other times to the left; and this in an incurvated line, which is convex towards that plane: so that the motion of a bullet is frequently in a line having a double curvature, it being bent towards the horizon by the force of gravity, and again bent out of its original direction to the right or left by some other force: in this case no part of the motion of the bullet is performed in the same plane, but its track will lie in the surface of a kind of cylinder, whose axis is perpendicular to the horizon.

"This proposition may be indubitably proved by the experience of every one in the least conversant with the practice of gunnery. The same piece which will carry its bullet within an inch of the intended mark at 10 yards distance, cannot be relied on to 10 inches in 100 yards, much less to 30 inches in 300 yards. Now this inequality can only arise from the track of the bullet being incurvated sideways as well as downwards: for by this means the distance between that incurvated line and the line of direction will increase in a much greater ratio than that of the distance; these lines being coincident at the mouth of the piece, and afterwards separating in the manner of a curve and its tangent, if the mouth of the piece be considered as the point of contact.—To put this matter out of all doubt, however, I took a barrel carrying a ball ¾ of an inch diameter, and fixing it on a heavy carriage, I satisfied myself of the steadiness and truth of its direction, by firing at a board 1½ feet square, which was placed at 180 feet distance; for I found, that in 16 successive shots I missed the mark but once. Now, the same barrel being fixed on the same carriage, and fired with a smaller quantity of powder, so that the shock on the discharge would be much less, and consequently the direction less changed, I found, that at 760 yards distance the ball flew sometimes 100 yards to the right of the line it was pointed on, and sometimes as much to the left. I found, too, that its direction in the perpendicular line was not less uncertain, it falling one time above 200 yards short of what it did at another; although, by the nicest examination of the piece after the discharge, it did not appear to have started in the least from the position it was placed in.

"The reality of this doubly curved track being thus demonstrated, it may perhaps be asked, What can be the cause of a motion so different from what has been hitherto supposed? And to this I answer, That the deflection in question must be owing to some power acting obliquely to the progressive motion of the body; body; which power can be no other than the resistance of the air. If it be farther asked, how the resistance of the air can ever come to be oblique to the progressive motion of the body? I farther reply, that it may sometimes arise from inequalities in the resisting surface; but that its general cause is doubtless a whirling motion acquired by the bullet about its axis: for by this motion of rotation, combined with the progressive motion, each part of the bullet's surface will strike the air very differently 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 as the motion of the bullet is greater in proportion to its progressive one.

"This whirling motion undoubtedly arises from the friction of the bullet against the sides of the piece; and as the rotatory motion will in some part of its revolution confine with the progressive one, 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 confines with the progressive one, and diminished where it is opposed to it: and by this means the whole effect of the resistance, instead of being opposite to the direction of the body, will become oblique thereto, and will produce those effects already mentioned. If it was possible to predict the position of the axis round which the bullet should whirl, and if that axis was unchangeable during the whole flight of the bullet, then the aberration of the bullet by this oblique force would be in a given direction; and the incursion produced thereby would regularly extend the same way from one end of its track to the other. For instance, if the axis of the whirl was perpendicular to the horizon, then the incursion would be to the right or left. If that axis was horizontal, and perpendicular to the direction of the bullet, then the incursion would be upwards or downwards. But as the first position of this 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, or tending to the same side in one part of its track that it does in another, but more usually is continually changing the tendency of its deflection, as the axis round which it whirls must frequently shift its position to the progressive motion by many inevitable accidents.

"That a bullet generally acquires such a rotatory motion, as here described, is, I think, demonstrable; however, to leave no room for doubt or dispute, I confirmed it, as well as some other parts of my theory, by the following experiments.

"I caused the machine to be made represented Plate CCXXV. fig. 4. BCDE is a brass barrel, moveable on its axis, and so adjusted by means of friction-wheels, not represented in the figure, as to have no friction worth attending to. The frame in which this barrel is fixed is so placed that its axis may be perpendicular to the horizon. The axis itself is continued above the upper plate of the frame, and has fastened on it a light hollow cone, AFG. From the lower part of this cone there is extended a long arm of wood, GH, which is very thin, and cut feather-edged. At its extremity there is a contrivance for fixing on the body, whose resistance is to be investigated (as here the globe P); and to prevent the arm GH from swaying out of its horizontal position by the weight of the annexed body P, there is a brace, AH, of fine wire, fastened to the top of the cone which supports the end of the arm.

"Round the barrel BCDE, there is wound a fine silk line, the turns of which appear in the figure; and after this line hath taken a sufficient number of turns, it is conducted nearly in a horizontal direction to the pully L over which it is passed, and then a proper weight M is hung to its extremity. If this weight be left at liberty, it is obvious that it will descend by its own gravity, and will, by its descent, turn round the barrel BCDE, together with the arm GH, and the body P fastened to it. And whilst the resistance on the arm GH and on the body P is less than the weight M, that weight will accelerate its motion; and thereby the motion of GH and P will increase, and consequently their resistance will increase, till at last this resistance and the weight M become nearly equal to each other. The motion with which M descends, and with which P revolves, will not then sensibly differ from an equable one. Whence it is not difficult to conceive, that, by proper observations made with this machine, the resistance of the body P may be determined. The most natural method of proceeding in this investigation is as follows: Let the machine first have acquired its equable motion, which it will usually do in about five or six turns from the beginning; and then let it be observed, by counting a number of turns, what time is taken up by one revolution of the body P: then taking off the body P and the weight M, let it be examined what smaller weight will make the arm GH revolve in the same time as when P was fixed to it: this smaller weight being taken from M, the remainder is obviously equal in effort to the resistance of the revolving body P; and this remainder being reduced in the ratio of the length of the arm to the semi-diameter of the barrel, will then become equal to the absolute quantity of the resistance. And as the time of one revolution is known, and consequently the velocity of the revolving body, there is hereby discovered the absolute quantity of the resistance to the given body P moving with a given degree of celerity.

"Here, to avoid all objections, I have generally chose, when the body P was removed, to fix in its stead a thin piece of lead of the same weight, placed horizontally; so that the weight which was to turn round the arm GH, without the body P, did also carry round this piece of lead. But mathematicians will easily allow that there was no necessity for this precaution.—The diameter of the barrel BCDE, and of the silk string wound round it, was 2.06 inches. The length of the arm GH, measured from the axis to the surface of the globe P, was 49.5 inches. The body P, the globe made use of, was of pasteboard; its surface very neatly coated with marbled paper. It was not much distant from the size of a 12 lb. shot, being in diameter 4.5 inches, so that the radius of the circle described by the centre of the globe was 51.75 inches. When this globe was fixed at the end of the arm, and a weight of half a pound was hung at the end of the string at M, it was examined how soon the motion of the descending weight M, and of the revolving body P, would become equable as to sense. With this view, three..." Theory three revolutions being suffered to elapse, it was found that the next 10 were performed in $27\frac{3}{4}$', 20 in less than 55", and 30 in $82\frac{1}{2}$'; so that the first 10 were performed in $27\frac{3}{4}$', the second in $27\frac{1}{2}$', and the third in $27\frac{1}{2}$'.

These experiments sufficiently evince, that even with half a pound, the smallest weight made use of, the motion of the machine was sufficiently equable after the first three revolutions.

The globe above mentioned being now fixed at the end of the arm, there was hung on at M a weight of $\frac{3}{4}$ lb.; and 10 revolutions being suffered to elapse, the succeeding 20 were performed in $21\frac{1}{2}'$. Then the globe being taken off, and a thin plate of lead, equal to it in weight, placed in its room; it was found, that instead of $\frac{3}{4}$ lb. a weight of one pound would make it revolve in less time than it did before; performing now 20 revolutions after 10 were elapsed in the space of $19\frac{1}{2}'$.

Hence then it follows, that from the $\frac{3}{4}$ lb. first hung on, there is less than 1 lb. to be deducted for the resistance on the arm; and consequently the resistance on the globe itself is not less than the effort of $2\frac{1}{4}$ lb. in the situation M; and it appearing from the former measures, that the radius of the barrel is nearly $\frac{3}{5}$ of the radius of the circle, described by the centre of the globe; it follows, that the absolute resistance of the globe, when it revolves 20 times in $21\frac{1}{2}'$, (about 25 feet in a second), is not less than the 50th part of two pounds and a quarter, or of 36 ounces; and this being considerably more than half an ounce, and the globe nearly the size of a twelve-pound shot, it irrefragably confirms a proposition I had formerly laid down from theory, that the resistance of the air to a 12 lb. iron shot, moving with a velocity of 25 feet in a second, is not less than half an ounce.

The rest of the experiments were made in order to confirm another proposition, namely, that the resistance of the air within certain limits is nearly in the duplicate proportion of the velocity of the resisting body. To investigate this point, there were successively hung on at M, weights in the proportion of the numbers 1, 4, 9, 16; and letting 10 revolutions first elapse, the following observations were made on the rest.—With $\frac{1}{2}$ lb. the globe went 20 turns in $54\frac{3}{4}'$, with 2 lb. it went 20 turns in $27\frac{1}{2}'$, with 4$\frac{1}{2}$ lb. it went 30 turns in $27\frac{1}{2}'$, and with 8 lb. it went 40 turns in $27\frac{1}{2}'$.—Hence it appears, that to resistances proportioned to the numbers 1, 4, 9, 16, there correspond velocities of the resisting body in the proportion of the numbers 1, 2, 3, 4; which proves, with great nicety, the proposition above mentioned.

With regard to the rotatory motion, the first experiment was to evince, that the whirling motion of a ball combining with its progressive motion would produce such an oblique resistance and deflective power as already mentioned. For this purpose a wooden ball of 4$\frac{1}{2}$ inches diameter was suspended by a double string, about eight or nine feet long. Now, by turning round the ball and twisting the double string, the ball when left to itself would have a revolving motion given it from the untwisting of the string again. And if, when the string was twisted, the ball was drawn to a considerable distance from the perpendicular, and there let go; it would at first, before it had acquired its revolving motion, vibrate steadily enough in the same vertical plane in which it first began to move: but when, by the untwisting of the string, it had acquired a sufficient degree of its whirling motion, it constantly deflected to the right or left of its first track; and sometimes proceeded so far as to have its direction at right angles to that in which it began its motion; and this deviation was not produced by the string itself, but appeared to be entirely owing to the resistance being greater on the one part of the leading surface of the globe than the other. For the deviation continued when the string was totally untwisted; and even during the time that the string, by the motion the globe had received, was twisting the contrary way. And it was always easy to predict, before the ball was let go, which way it would deflect, only by considering on which side the whirl would be combined with the progressive motion; for on that side always the deflective power acted, as the resistance was greater here than on the side where the whirl and progressive motion were opposed to one another.

Though Mr Robins considered this experiment as an incontestable proof of the truth of his theory, he undertook to give ocular demonstration of this deflection of musket-bullets even in the short space of 100 yards.

As all projectiles," says he, "in their flight, are acted upon by the power of gravity, the deflection of a bullet from its primary direction, supposes that deflection to be upwards or downwards in a vertical plane; because, in the vertical plane, the action of gravity is compounded and entangled with the deflective force. And for this reason my experiments have been principally directed to the examination of that deflection which carries the bullet to the right or left of that plane in which it began to move. For if it appears at any time that the bullet has shifted from that vertical plane in which the motion began, this will be an incontestable proof of what we have advanced.—Now, by means of screens of exceeding thin paper, placed parallel to each other at proper distances, this deflection in question may be many ways investigated. For by firing bullets which shall traverse the screens, the flight of the bullet may be traced; and it may easily appear whether they do or do not keep invariably to one vertical plane. This examination may proceed on three different principles, which I shall here separately explain.

For first, an exactly vertical plane may be traced out upon all these screens, by which the deviation of any single bullet may be more readily investigated, only by measuring the horizontal distance of its trace from the vertical plane thus delineated; and by this means the absolute quantity of its aberration may be known. Or if the description of such a vertical plane should be deemed a matter of difficulty and nicety, a second method may be followed; which is that of resting the piece in some fixed notch or socket, so that though the piece may have some little play to the right and left, yet all the lines in which the bullet can be directed shall intersect each other in the centre of that fixed socket; by this means, if two different shots are fired from the piece thus situated, the horizontal distances made by the two bullets on any two screens ought to be in the same proportion to each other as the respective distances of the screens from the socket in which the piece was laid. And if these horizontal distances differ from that proportion, then it is certain that one of the shot at least hath deviated from a vertical plane, although the absolute quantity of that deviation cannot hence be assigned; because it cannot be known what part of it is to be imputed to one bullet, and what to the other.

"But if the constant and invariable position of the notch or socket in which the piece was placed, be thought too hard an hypothesis in this very nice affair; the third method, and which is the simplest of all, requires no more than that two shot be fired through three screens without any regard to the position of the piece each time: for in this case, if the shots diverge from each other, and both keep to a vertical plane, then if the horizontal distances of their traces on the first screen be taken from the like horizontal distances on the second and third, the two remainders will be in the same proportion with the distances of the second and third screen from the first. And if they are not in this proportion, then it will be certain that one of them at least hath been deflected from the vertical plane; though here, as in the last case, the quantity of that deflection in each will not be known.

"All these three methods I have myself made use of at different times, and have ever found the success agreeable to my expectation. But the most eligible method seemed to be a compound of the two last. The apparatus was as follows.—Two screens were set up in the larger walk in the charter-house garden; the first of them at 250 feet distance from the wall, which was to serve for a third screen; and the second 200 feet from the same wall. At 50 feet before the first screen, or at 300 feet from the wall, there was placed a large block weighing about 200 lb. weight, and having fixed into it an iron bar with a socket at its extremity, in which the piece was to be laid. The piece itself was of a common length, and bored for an ounce ball. It was each time loaded with a ball of 17 to the pound, so that the windage was extremely small, and with a quarter of an ounce of good powder. The screens were made of the thinnest flue paper; and the resistance they gave to the bullet (and consequently their probability of deflecting it) was so small, that a bullet lighting one time near the extremity of one of the screens, left a fine thin fragment of it towards the edge entire, which was so very weak that it was difficult to handle it without breaking. These things thus prepared, five shot were made with the piece rested in the notch above mentioned; and the horizontal distances between the first shot, which was taken as a standard, and the four succeeding ones, both on the first and second screen and on the wall, measured in inches, were as follows:

| 1st Screen | 2nd Screen | Wall | |------------|------------|------| | 1 to 2 | 175 R. | 315 R. | 167 R. | | 3 | 10 L. | 156 L. | 6925 L. | | 4 | 125 L. | 45 L. | 150 L. | | 5 | 215 L. | 51 L. | 190 L. |

Here the letters R and L denote that the shot in question went either to the right or left of the first.

"If the position of the socket in which the piece was placed be supposed fixed, then the horizontal distances measured above on the first and second screen, and on the wall, ought to be in proportion to the distances of the first screen, the second screen, and the wall from the socket. But by only looking over these numbers, it appears, that none of them are in that proportion; the horizontal distance of the first and third, for instance, on the wall being above nine inches more than it should be by this analogy.

"If, without supposing the invariable position of the socket, we examine the comparative horizontal distances according to the third method described above, we shall in this case discover diversifications still more extraordinary; for, by the numbers set down, it appears, that the horizontal distances of the second and third shot on the two screens, and on the wall, are as under.

| 1st Screen | 2nd Screen | Wall | |------------|------------|------| | 11.75 | 18.75 | 83.95 |

Here, if, according to the rule given above, the distance on the first screen be taken from the distances on the other two, the remainder will be 7, and 74.2; and these numbers, if each shot kept to a vertical plane, ought to be in the proportion of 1 to 5; that being the proportion of the distances of the second screen, and of the wall from the first; but the last number 74.2 exceeds what it ought to be by this analogy by 39.2; so that between them there is a deviation from the vertical plane of above 39 inches, and this too in a transit of little more than 80 yards.

"But farther, to show that these irregularities do not depend on any accidental circumstance of the balls fitting or not fitting the piece, there were five shots more made with the same quantity of powder as before; but with smaller bullets, which ran much looser in the piece. And the horizontal distances being measured in inches from the trace of the first bullet to each of the succeeding ones, the numbers were as under.

| 1st Screen | 2nd Screen | Wall | |------------|------------|------| | 1 to 2 | 15.6 R. | 31.1 R. | 94.0 R. | | 3 | 6.4 L. | 12.75 L. | 23.0 L. | | 4 | 4.7 R. | 8.5 R. | 15.5 R. | | 5 | 12.6 R. | 24.0 R. | 63.5 R. |

Here, again, on the supposed fixed position of the piece, the horizontal distance on the wall between the first and third will be found above 15 inches less than it should be if each kept to a vertical plane; and like irregularities, though smaller, occur in every other experiment. And if they are examined according to the third method set down above, and the horizontal distances of the third and fourth, for instance, are compared, those on the first and second screen, and on the wall, appear to be thus.

| 1st Screen | 2nd Screen | Wall | |------------|------------|------| | 11.1 | 21.25 | 38.5 |

And if the horizontal distance on the first screen be taken from the other two, the remainders will be 10.15, and 27.4; where the least of them, instead of being five times the first, as it ought to be, is 23.35 short of it; so that here is a deviation of 23 inches.

"From all these experiments, the defection in question seems to be incontrovertibly evinced. But to give some farther light to this subject, I took a barrel of the same bore with that hitherto used; and bent it at about three or four inches from its muzzle to the left, the bend making an angle of three or four degrees with with the axis of the piece. This piece thus bent was fired with a loose ball, and the same quantity of powder hitherto used, the screens of the last experiment being still continued. It was natural to expect, that if this piece was pointed by the general direction of its axis, the ball would be canted to the left of that direction by the bend near its mouth. But as the bullet, in passing through that bent part, would, as I conceived, be forced to roll upon the right-hand side of the barrel, and thereby its left side would turn up against the air, and would increase the resistance on that side; I predicted to the company then present, that if the axis on which the bullet whirled, did not shift its position after it was separated from the piece; then, notwithstanding the bent of the piece to the left, the bullet itself might be expected to incurvate towards the right; and this, upon trial, did most remarkably happen. For one of the bullets fired from this bent piece passed through the first screen about \(1\frac{1}{2}\) inch distant from the trace of one of the shot fired from the straight piece in the last set of experiments. On the second screen, the traces of the same bullets were about three inches distant; the bullet from the crooked piece passing on both screens to the left of the other: but comparing the places of these bullets on the wall, it appeared that the bullet from the crooked piece, though it diverged from the track on the two screens, had now crossed that track, and was deflected considerably to the right of it; so that it was obvious, that though the bullet from the crooked piece might first be canted to the left, and had diverged from the track of the other bullet with which it was compared, yet by degrees it deviated again to the right, and a little beyond the second screen crossed that track from which it before diverged, and on the wall was deflected 14 inches, as I remember, on the contrary side. And this experiment is not only the most convincing proof of the reality of this deflection here contended for; but is likewise the strongest confirmation that it is brought about in the very manner and by the very circumstances which we have all along described.

"I have now only to add, that as I suspected the consideration of the revolving motion of the bullet, compounded with its progressive one, might be considered as a subject of mathematical speculation, and that the reality of any deflecting force thence arising might perhaps be deduced by some computations upon the principles hitherto received of the action of fluids; I thought proper to annex a few experiments, with a view of evincing the strange deficiency of all theories of this fort hitherto established, and the unexpected and wonderful varieties which occur in these matters: The proposition which I advanced for this purpose being, That two equal surfaces meeting the air with the same degree of obliquity, may be so differently resisted, that though in one of them the resistance is less than that of a perpendicular surface meeting the same quantity of air, yet in another it shall be considerably greater.

"To make out this proposition, I made use of the machine already described; and having prepared a pasteboard pyramid, whose base was four inches square, and whose planes made angles of 45° with the plane of its base; and also a parallelogram four inches in breadth, and 5½ inches in length, which was equal to the surface of the pyramid, the globe P was taken off from the machine, and the pyramid was first fixed on; and 2 lb. being hung at M, and the pyramid so fitted as to move with its vertex forwards, it performed 20 revolutions after the first ten were elapsed in 33½". Then the pyramid being turned, so that its base, which was a plane of four inches square, went foremost, it now performed 20 revolutions with the same weight in 38½".—After this, taking off the pyramid, and fixing on the parallelogram with its longer side perpendicular to the arm, and placing its surface in an angle of 45° with the horizon by a quadrant, the parallelogram, with the same weight, performed 20 revolutions in 43½".

"Now here this parallelogram and the surface of the pyramid are equal to each other, and each of them met the air in an angle of 45°; and yet one of them made 20 revolutions in 33½", whilst the other took up 43½". And at the same time it appears, that a flat surface, such as a base of a pyramid, which meets the same quantity of air perpendicularly, makes 20 revolutions in 38½", which is the medium between the other two.

"But to give another and still more simple proof of this principle; there was taken a parallelogram four inches broad and 8½ long. This being fixed at the end of the arm, with its long side perpendicular thereto, and being placed in an angle of 45° with the horizon, there was a weight hung on at M of 3½ lb. with which the parallelogram made 20 revolutions in 40½". But after this, the position of the parallelogram was shifted, and it was placed with its shorter side perpendicular to the arm, though its surface was still inclined to an angle of 45° with the horizon; and now, instead of going slower, as might be expected from the greater extent of part of its surface from the axis of the machine, it went round much faster: for in this last situation it made 20 revolutions in 35½", so that there were 5" difference in the time of 20 revolutions; and this from no other change of circumstance than as the larger or shorter side of the oblique plane was perpendicular to the line of its direction."

In the 73rd volume of the Philosophical Transactions, several experiments on this subject, but upon a larger scale, are related by Lovell Edgeworth, Esq. They confirm the truth of what Mr Robins advances, but nothing is said to explain the reason of it.

These are the principal experiments made by Mr Whyte Robins in confirmation of his theory, and which not art of gunnery to its ne plus ultra. It must be observed, however, that in this art it is impossible we should ever arrive at absolute perfection; that is, it can never be expected that a gunner, by any method of calculation whatever, could be enabled to point his guns in such a manner, that the shot would hit the mark if placed anywhere within its range. Aberrations, which can by no means be either foreseen or prevented, will take place from a great number of different causes. A variation in the density of the atmosphere, in the dampness of the powder, or in the figure of the shot, will cause variations in the range of the bullet, which cannot by any means be reduced to rules, and consequently must must render the event of each shot very precarious. The resistance of the atmosphere simply considered, without any of those anomalies arising from its density at different times, is a problem which, notwithstanding the labours of Mr Robins and others, hath not been completely solved; and, indeed, if we consider the matter in a physical light, we shall find, that without some other data than those which are yet obtained, an exact solution of it is impossible.

It is an objection that hath been made to the mathematical philosophy, and to which in many cases it is most certainly liable, that it confounds the resistance of matter more than its capacity of giving motion to other matter. Hence, if in any case matter acts both as a resisting and a moving power, and the mathematician overlooks its effort towards motion, founding his demonstrations only upon its property of resisting, these demonstrations will certainly be false, tho' they should be supported by all the powers of geometry. It is an error of this kind that we are to attribute the great differences already taken notice of between the calculations of Sir Isaac Newton, with regard to the resisting force of fluids, and what actually takes place upon trial. These calculations were made upon the supposition that the fluid through which a body moved could do nothing else but resist it; yet it is certain, that the air (the fluid with which we have to do at present) proves a source of motion, as well as resistance, to all bodies which move in it.

To understand this matter fully, let ABC represent a crooked tube made of any solid matter, and a, b, two pistons which exactly fill the cavity. If the space between these pistons is full of air, it is plain they cannot come into contact with each other on account of the elasticity of the included air, but will remain at some certain distance as represented in the figure. If the piston b is drawn up, the air which presses in the direction Cb acts as a resisting power, and the piston will not be drawn up with such ease as if the whole was in vacuo. But though the column of air pressing in the direction Cb acts as a resisting power on the piston b, the column pressing in the direction Aa will act as a moving power upon the piston a. It is therefore plain, that if b is moved upwards till it comes to the place marked d, the other will descend to that marked c. Now, if we suppose the piston a to be removed, it is plain, that when b is pulled upwards to d, the air descending through the leg AaCB will press on the under side of the piston b, as strongly as it would have done upon the upper side of the piston a, had it been present. Therefore, though the air passing down through the leg CB resists the motion of the piston b when drawn upwards, the air pressing down through the leg AB forwards it as much; and accordingly the piston b may be drawn up or pushed down at pleasure, and with very little trouble. But if the orifice at A is stopped, so that the air can only exert its resisting power on the piston b, it will require a considerable degree of strength to move the piston from b to d.

If now we suppose the tube to be entirely removed (which indeed answers no other purpose than to render the action of the air more evident), it is plain, that if the piston is moved either up or down, or in any other direction we can imagine, the air presses as much upon the back part of it as it resists it on the fore part; and of consequence, a ball moving through the air with any degree of velocity, ought to be as much accelerated by the action of the air behind, as it is retarded by the action of that before.—Here then it is natural to ask, If the air accelerates a moving body as much as it retards it, how comes it to make any resistance at all? yet certain it is, that this fluid doth resist, and that very considerably. To this it may be answered, that the air is always kept in some certain state or constitution by another power which rules all its motions, and it is this power undoubtedly which gives the resistance. It is not to our purpose at present to inquire what that power is; but we see that the air is often in very different states: one day, for instance, its parts are violently agitated by a storm; and another, perhaps, they are comparatively at rest in a calm. In the first case, nobody hesitates to own, that the storm is occasioned by some cause or other, which violently resists any other power that would prevent the agitation of the air. In a calm, the case is the same; for it would require the same exertion of power to excite a tempest in a calm day, as to allay a tempest in a stormy one. Now it is evident, that all projectiles, by their motion, agitate the atmosphere in an unnatural manner; and consequently are resisted by that power, whatever it is, which tends to restore the equilibrium, or bring back the atmosphere to its former state.

If no other power besides that above mentioned acted upon projectiles, it is probable, that all resistance to their motion would be in the duplicate proportion of their velocities; and accordingly, as long as the velocity is small, we find it generally is so. But when the velocity comes to be exceedingly great, other forces of resistance arise. One of these is a subtraction of part of the moving power; which though not properly a resistance, or opposing another power to it, is an equivalent thereto. This subtraction arises from the following cause. The air, as we have already observed, presses upon the hinder part of the moving body by its gravity, as much as it resists the forepart of it by the same property. Nevertheless, the velocity with which the air presses upon any body by means of its gravity, is limited; and it is possible that a body may change its place with so great velocity that the air hath not time to rush in upon the back part of it, in order to assist its progressive motion. When this happens to be the case, there is in the first place a deficiency of the moving power equivalent to 15 pounds on every square inch of surface; at the same time that there is a positive resistance of as much more on the forepart, owing to the gravity of the atmosphere, which must be overcome before the body can move forward.

This deficiency of moving power, and increase of resistance, do not only take place when the body moves with a very great degree of velocity, but in all motions whatever. It is not in all cases perceptible, because the velocity with which the body moves, frequently bears but a very small proportion to the velocity with which the air presses in behind it. Thus, supposing the velocity with which the air rushes into a vacuum to be 1200 feet in a second, if a body moves with a velocity of 30, 40, or 50 feet in a second, the force with which the air presses on the back part is but $\frac{1}{4}$ at the utmost less than that which resists on the forepart of it, which Theory, which will not be perceptible: but if, as in the case of bullets, the velocity of the projectile comes to have a considerable proportion to the velocity wherewith the air rushes behind it; then a very perceptible and otherwise unaccountable resistance is observed, as we have seen in the experiments already related by Mr Robins. Thus, if the air presses in with a velocity of 1200 feet in a second, if the body changes its place with a velocity of 600 feet in the same time, there is a resistance of 15 pounds on the fore part, and a pressure of only \( \frac{7}{4} \) pounds on the back part. The resistance therefore not only overcomes the moving power of the air by \( \frac{7}{4} \) pounds, but there is a deficiency of other \( \frac{7}{4} \) pounds owing to the want of half the pressure of the atmosphere on the back part, and thus the whole loss of the moving power is equivalent to 15 pounds; and hence the exceeding great increase of resistance observed by Mr Robins beyond what it ought to be according to the common computations.—The velocity with which the air rushes into a vacuum is therefore a desideratum in gunnery. Mr Robins supposes that it is the same with the velocity of sound; and that when a bullet moves with a velocity greater than that of 1200 feet in a second, it leaves a perfect vacuum behind it. Hence he accounts for the great increase of resistance to bullets moving with such velocities; but as he doth not take notice of the loss of the air's moving power, the anomalies of all lesser velocities are inexplicable on his principles. Nay, he even tells us, that Sir Isaac Newton's rule for computing resistances may be applied in all velocities less than 1100 or 1200 feet in a second, though this is expressly contradicted by his own experiments mentioned n° 23.

Though for these reasons it is evident how great difficulties must occur in attempting to calculate the resistance of the air to military projectiles, we have not yet discovered all the sources of resistance to these bodies when moving with immense velocities. Another power by which they are opposed (and which at last becomes greater than any of those hitherto mentioned), is the air's elasticity. This, however, will not begin to show itself in the way of resistance till the velocity of the moving body becomes considerably greater than that by which the air presses into a vacuum. Having therefore first ascertained this velocity, which we shall suppose to be 1200 feet in a second, it is plain, that if a body moves with a velocity of 1800 feet in a second, it must compress the air before it; because the fluid hath neither time to expand itself in order to fill the vacuum left behind the moving body, nor to rush in by its gravity. This compression it will resist by its elastic power, which thus becomes a new source of resistance, increasing without any limit, in proportion to the velocity of the moving body. If now we suppose the moving body to set out with a velocity of 2400 feet in a second, it is plain, that there is not only a vacuum left behind the body, but the air before it is compressed into half its natural space. The loss of motion in the projectile therefore is now very considerable. It first loses 15 pounds on every square inch of surface on account of the deficiency of the moving power of the air behind it; then it loses 15 pounds more on account of the resistance of the air before it; again it loses 15 pounds on account of the elasticity of the compressed air; and lastly another 15 pounds on account of the vacuum behind, which takes off the weight of the atmosphere, that would have been equivalent to one half of the elasticity of the air before it. The whole resistance therefore upon every square inch of surface moving with this velocity is 60 pounds, besides that which arises from the power tending to preserve the general state of the atmosphere, and which increases in the duplicate proportion of the velocity as already mentioned. If the body is supposed to move with a velocity of 4800 feet in a second, the resistance from the air's elasticity will then be quadrupled, or amount to 60 pounds on the square inch of surface; which added to the other causes, produces a resistance of 105 pounds upon the square inch; and thus would the resistance from the elasticity of the air go on continually increasing, till at last the motion of the projectile would be as effectually stopped as if it was fired against a wall. This obstacle therefore we are to consider as really insuperable by any art whatever, and therefore it is not advisable to use larger charges of powder than what will project the shot with a velocity of 1200 feet in a second. To this velocity the elasticity of the air will not make great resistance, if indeed it do make any at all: for though Mr Robins hath conjectured that air rushes into a vacuum with the velocity of sound, or between 11 and 1200 feet in a second; yet we have no decisive proof of the truth of this supposition. At this velocity indeed, according to Mr Robins, a very sudden increase of resistance takes place: but this is denied by Mr Glenie *, who supposes that the resistance proceeds gradually; and indeed it seems to be pretty obvious, that the resistance cannot very suddenly increase, if the velocity is only increased in a small degree. Yet it is certain, that the swiftest motions with which cannon-balls can be projected are very soon reduced to this standard; for Mr Robins acquaints us, that "a 24-pound shot, when discharged with a velocity of 2000 feet in a second, will be reduced to that of 1200 feet in a second in a flight of little more than 500 yards."

In the 71st volume of the Philosophical Transactions, Mr Thomson has proposed a new method of determining the velocities of bullets, by measuring the force of the recoil of the piece. As in all cases action and reaction are supposed to be equal to one another, it appears that the momentum of a gun, or the force of its recoil backwards, must always be equivalent to the force of its charge: that is, the velocity with which the gun recoils, multiplied into its weight, is equal to the velocity of the bullet multiplied into its weight; for every particle of matter, whether solid or fluid, that flies out of the mouth of a piece, must be impelled by the action of some power, which power must react with equal force against the bottom of the bore.—Even the fine invisible elastic fluid that is generated from the powder in its inflammation, cannot put itself in motion without reacting against the gun at the same time. Thus we see pieces, when they are fired with powder alone, recoil as well as when their charges are made to impel a weight of shot, though the recoil is not in the same degree in both cases. It is easy to determine the velocity of the recoil in any given case, by suspending the gun in a horizontal position by two pendulous rods, and measuring the arc of its ascent by means of a ribbon, as mentioned under... the article Gunpowder; and this will give the momentum of the gun, its weight being known, and consequently the momentum of its charge. But in order to determine the velocity of the bullet from the momentum of the recoil, it will be necessary to know how much the weight and velocity of the elastic fluid contributes to it.

"That part of the recoil which arises from the expansion of the fluid is always very nearly the same whether the powder is fired alone, or whether the charge is made to impel one or more bullets, as has been determined by a great variety of experiments.—If therefore a gun, suspended according to the method prescribed, is fired with any given charge of powder, but without any bullet or wad, and the recoil is observed, and if the same piece is afterwards fired with the same quantity of powder, and a bullet of a known weight, the excess of the velocity of the recoil in the latter case, over that in the former, will be proportional to the velocity of the bullet; for the difference of these velocities, multiplied into the weight of the gun, will be equal to the weight of the bullet multiplied into its velocity.—Thus, if W is put equal to the weight of the gun, U = the velocity of the bullet when fired with a given charge of powder without any bullet; V = the velocity of the recoil, when the same charge is made to impel a bullet; B = the weight of the bullet, and v = its velocity; it will be \( \frac{V - U + W}{B} \).

To determine how far this theory agreed with practice, an experiment was made with a charge of 165 grains of powder without any bullet, which produced a recoil of 5.5 inches; and in another, with a bullet, the recoil was 5.6 inches; the mean of which is 5.55 inches; answering to a velocity of 1.1358 feet in a second. In five experiments with the same charge of powder, and a bullet weighing 580 grains, the mean was 14.6 inches; and the velocity of the recoil answering to the length just mentioned, is 2.9880 feet in a second: consequently \( V - U \), or 2.9880 - 1.1358, is equal to 1.8522 feet in a second. But as the velocities of recoil are known to be as the chords of the arcs through which the barrel ascends, it is not necessary, in order to determine the velocity of the bullet, to compute the velocities V and U; but the quantity \( V - U \), or the difference of the velocities of the recoil when the given charge is fired with and without a bullet, may be computed from the value of the difference of the chords by one operation.—Thus the velocity answering to the chord 9.05, is that of 1.8522 feet in a second, is just equal to \( V - U \), as was before found.

In this experiment the weight of the barrel with its carriage was just 47½ pounds, to which \( \frac{1}{4} \) of a pound were to be added on account of the weight of the rods by which it was suspended; which makes W = 48 pounds, or 336,000 grains. The weight of the bullet was 580 grains; whence B is to W as 580 to 336,000; that is, as 1 to 579.31 very nearly. The value of \( V - U \), answering to the experiments before mentioned, was found to be 1.8522; consequently the velocity of the bullets \( v_w \) was 1.8522 + 579.31 = 1073 feet, which differs only by 10 from 1083, the velocities found by the pendulum.

The velocities of the bullets may be found from the

\[ \frac{V - U + W}{B} \]

which measures the velocity of the bullet, the ratio of W to B remaining the same.—If therefore we suppose a case in which C - c is equal to one inch, and the velocity of the bullet is computed from that chord, the velocity in any other case, wherein C - c is greater or less than one inch, will be found by multiplying the difference of the chords C and c by the velocity that answers to the difference of one inch.—The length of the parallel rods, by which the piece was suspended being 64 inches, the velocity of the recoil, \( C - c = 1 \) inch measured upon the ribbon, is 0.204655 parts of a foot in one second; which in this case is also the value of \( V - U \); the velocity of the bullet, or \( v_w \) is therefore 0.204655 + 579.31 = 118.35 feet in a second. Hence the velocity of the bullet may in all cases be found by multiplying the difference of the chords C and c by 118.35; the weight of the barrel, the length of the rods by which it is suspended, and the weight of the bullet remaining the same; and this whatever the charge of powder made use of may be, and however it may differ in strength and goodness.

The exactness of this second method will appear from the following experiments. On firing the piece with 145 grains of powder and a bullet, the mean of three sets of experiments was 13.25, 13.15, and 13.2; and with the same charge of powder without a bullet, the recoil was 4.5, 4.3, or 4.4; \( C - c \) therefore was 13.2 - 4.4 = 8.8 inches; and the velocity of the bullets \( = 8.8 + 118.35 = 1045 \) feet in a second; the velocities by the pendulum coming out 1040 feet in the same space of time.

In the far greatest number of experiments to determine the comparative accuracy of the two methods, a surprising agreement was found between the last mentioned one and that by the pendulum; but in some few the differences were very remarkable. Thus, in two where the recoil was 12.92, and 13.28 the velocity, by computation from the chords is 1030 feet per second; but in computing by the pendulum it amounted only to 900; but in these some inaccuracy was suspected in the experiment with the pendulum, and that the computation from the recoil was most to be depended upon. In another experiment, the velocity by the recoil exceeded that by the pendulum by no less than 346 feet; the former showing 2109, and the latter only 1763 feet in a second. In two others the pendulum was also deficient, though not in such a degree. In all these it is remarkable, that where the difference was considerable, it was still in favour of the recoil. The deficiency in these experiments appears to have been somewhat embarrassing to our author. "It cannot be supposed, says he, that it arose from any imperfection in Mr Robins's method of determining the velocities of bullets; for that method is founded upon such principles as leave no room to doubt of its accuracy; and the practical errors that occur in making the experiments, and which cannot be entirely prevented, or exactly Theory. exactly compensated, are in general so small, that the difference in the velocities cannot be attributed to them. It is true, the effect of those errors is more likely to appear in experiments made under such circumstances as the present; for the bullet being very light (a), the arc of the ascent of the pendulum was but small; and a small mistake in measuring the chord upon the ribbon would have produced a very considerable error in computing the velocity of the bullet: Thus a difference of one-tenth of an inch, more or less, upon the ribbon, in that experiment where the difference was greatest, would have made a difference in the velocity of more than 120 feet in a second. But, independent of the pains that were taken to prevent mistakes, the striking agreement of the velocities in so many other experiments, affords abundant reason to conclude, that the errors arising from those causes were in no case very considerable.—But if both methods of determining the velocities of bullets are to be relied on, then the difference of the velocities, as determined by them in these experiments, can only be accounted for by supposing that it arose from their having been diminished by the resistance of the air in the passage of the bullets from the mouth of the piece to the pendulum; and this suspicion will be much strengthened, when we consider how great the resistance of the air is to bodies that move very swiftly in it; and that the bullets in these experiments were not only projected with great velocities, but were also very light, and consequently more liable to be retarded by the resistance on that account.

"To put the matter beyond all doubt, let us see what the resistance was that these bullets met with, and how much their velocities were diminished by it. The weight of the bullet in the most expensive experiment was 90 grains; its diameter 0.78 of an inch; and it was projected with a velocity of 2109 feet in a second. If now a computation be made according to the law laid down by Sir Isaac Newton for compressed fluids, it will be found, that the resistance to this bullet was not less than 8½ pounds avoirdupois, which is something more than 660 times its own weight. But Mr Robins has shown by experiment, that the resistance of the air to bodies moving in it with very great velocity, is near three times greater than Sir Isaac has determined it; and as the velocity with which this bullet was impelled is considerably greater than any in Mr Robins's experiments, it is highly probable, that the resistance in this instance was at least 2000 times greater than the weight of the bullet.

"The distance from the mouth of the piece to the pendulum was 12 feet; but, as there is reason to think that the blast of the powder, which always follows the bullet, continues to act upon it for some sensible space of time after it is out of the bore, and, by urging it on, counterbalances, or at least counteracts in a great measure, the resistance of the air, we will suppose that the resistance does not begin, or rather that the motion of the bullet does not begin to be retarded, till it has got to the distance of two feet from the muzzle. The distance, therefore, between the barrel and the pendulum, instead of 12 feet, is to be estimated at 10 feet; and as the bullet took up about \( \frac{1}{3} \) part of a second in running over that space, it must in that time have lost a velocity of about 335 feet in a second, as will appear upon making the computation; and this will very exactly account for the apparent diminution of the velocity in the experiment: for the difference of the velocities, as determined by the recoil and the pendulum, \( = 2109 - 1763 = 346 \) feet in a second, is extremely near 335 feet in a second, the diminution of the velocity by the resistance as here determined.

"If the diminution of the velocities of the bullets in the two subsequent experiments be computed in like manner, it will turn out in one 65, and in the other 33, feet in a second: and, making these corrections, the comparison of the two methods of ascertaining the velocities will stand thus:

| Velocities by the pendulum | 1763 | 1317 | 1136 | |----------------------------|------|------|------| | Resistance of air to be added | 335 | 65 | 33 | |-------------------------------|-----|----|----| | 2098 | 1382 | 1169 |

Velocity by the recoil

| 2109 | 1430 | 1288 |

Difference after correction, +11 +48 +119

"It appears therefore, that notwithstanding these corrections, the velocities as determined by the pendulum, particularly in the last, were considerably deficient. But the manifest irregularity of the velocities, in those instances, affords abundant reason to conclude, that it must have arisen from some accidental cause, and therefore that little dependence is to be put upon the result of those experiments. I cannot take upon me to determine positively what the cause was which produced this irregularity, but I strongly suspect that it arose from the breaking of the bullets in the barrel by the force of the explosion: for these bullets, as has already been mentioned, were formed of lead, inclosing lesser bullets of plaster of Paris; and I well remember to have observed at the time several small fragments of the plaster which had fallen down by the side of the pendulum. I confess I did not then pay much attention to this circumstance, as I naturally concluded that it arose from the breaking of the bullet in penetrating the target of the pendulum; and that the small pieces of plaster I saw upon the ground, had fallen out of the hole by which the bullet entered. But if the bullets were not absolutely broken in pieces in firing, yet if they were considerably bruised, and the plaster, or a part of it, were separated from the lead, such a change in the form might produce a great increase in the resistance, and even their initial velocities might be affected by it; for their form being changed from that of a globe to some other figure, they might not fit the bore; and a part of the force of the charge might be lost by the windage.—That this actually happened in the experiment last-mentioned, seems very probable; as the velocity with which the bullet was projected, as it was determined by the recoil, was considerably less in proportion in that experiment than in many others which preceded and followed it in the same set.

"As allowance has been made for the resistance of the air in these cases, it may be expected that the same should

(a) They were made of lead inclosing a nucleus of Paris plaster. should be done in all other cases; but it will probably appear, upon inquiry, that the diminution of the velocities of the bullets, on that account, was so inconsiderable, that it might safely be neglected; thus, for instance, in the experiments with an ounce of powder, when the velocity of the bullet was more than 1750 feet in a second, the diminution turns out no more than 25 or 30 feet in a second, though we suppose the full resistance to have begun so near as two feet from the mouth of the piece; and in all cases where the velocity was less, the effect of the resistance was less in a much greater proportion: and even in this instance, there is reason to think, that the diminution of the velocity, as we have determined it, is too great; for the flame of gunpowder expands with such amazing rapidity, that it is scarcely to be supposed but that it follows the bullet, and continues to act upon it more than two feet, or even four feet, from the gun; and when the velocity of the bullet is less, its action upon it must be sensible at a still greater distance."

As this method of determining the velocities of bullets by the recoil of the piece did not occur to Mr Thomson till after he had finished his experiments with a pendulum, and taken down his apparatus, he had it not in his power to determine the comparative strength of the recoil without and with a bullet; and consequently the velocity with which the flame issues from the mouth of a piece. He is of opinion, however, that every thing relative to these matters may be determined with greater accuracy by the new method than by any other formerly practised; and he very justly remarks, that the method of determining the velocity by the recoil, gives it originally as the bullet sets out; while that by the pendulum shows it only after a part has been destroyed by the resistance of the air. In the course of his remarks, he criticizes upon a part of Mr Robins's theory, that when bullets of the same diameter, but different weights, are discharged from the same piece by the same quantity of powder, their velocities are in a sub-duplicate ratio of their weight. This theory, he observes, is manifestly defective, as being founded upon a supposition, that the action of the elastic fluid, generated from the powder, is always the same in any and every given part of the bore when the charge is the same, whatever may be the weight of the bullet; and as no allowance is made for the expenditure of force required to put the fluid itself in motion, nor for the loss of it by the vent. "It is true (says he) Dr Hutton in his experiments found this law to obtain without any great error; and possibly it may hold good with sufficient accuracy in many cases; for it sometimes happens, that a number of errors or actions, whose operations have a contrary tendency, to compensate each other, that their effects when united are not sensible. But when this is the case, if any one of the causes of error is removed, those which remain will be detected.—When any given charge is loaded with a heavy bullet, more of the powder is inflamed in any very short space of time than when the bullet is lighter, and the action of the powder ought upon that account to be greater; but a heavy bullet takes up longer time in passing through the bore than a light one; and consequently more of the elastic fluid generated from the powder escapes by the vent and by windage.

It may happen that the augmentation of the force, on account of one of these circumstances, may be just able to counterbalance the diminution of it arising from the other; and if it should be found upon trial, that this is the case in general, in pieces as they are now constructed, and with all the variety of shot that are made use of in practice, it would be of great use to know the fact; but when, with Mr Robins, concluding too hastily from the result of a partial experiment, we suppose, that because the sum total of the pressure of the elastic fluid upon the bullet, during the time of its passage through the bore, happens to be the same when bullets of different weights are made use of, that therefore it is always so, our reasonings may prove very inconclusive, and lead to very dangerous errors."

In the prosecution of his subject Mr Thomson proves mathematically, as well as by actual experiment, that the theory laid down by Mr Robins in this respect is erroneous. The excess is in favour of heavy bullets, which acquire a velocity greater than they ought to do according to Mr Robins's rule; and so considerable are the errors, that in one of Mr Thomson's experiments, the difference was no less than 2042 feet in a second. When the weight of the bullet was increased four times, the action of the powder was found to be nearly doubled; for in one experiment, when four bullets were discharged at once, the collective pressure was as 1; but when only a single bullet was made use of, it was no more than 0.5825; and on the whole he concludes, that the velocity of bullets is in the reciprocal sub-triplicate ratio of their weights. Our author observes also, that Mr Robins is not only mistaken in the particular just mentioned, but in his conclusions with regard to the absolute force of gunpowder compared with the pressure of the atmosphere; the latter being to the force of gunpowder as 1 to 1000 according to Mr Robins; but as 1 to 1308 according to Mr Thomson.

Sect. III. Practice of Gunnery.

With regard to the practical part of gunnery, which ought to consist in directing the piece in such a manner as always to hit the object against which it is pointed, there can be no certain rules given. The following maxims are laid down by Mr Robins as of use in practice.

1. In any piece of artillery whatever, the greater the quantity of powder it is charged with, the greater will be the velocity of the bullet.

2. If two pieces of the same bore, but of different lengths, are fired with the same charge of powder, the longer will impel the bullet with a greater celerity than the shorter.

3. If two pieces of artillery different in weight, and formed of different metals, have yet their cylinders of equal bores and equal lengths; then with like charges of powder and like bullets they will each of them discharge their shot with nearly the same degree of celerity.

4. The ranges of pieces at a given elevation are not just measures of the velocity of the shot; for the same piece fired successively at an invariable elevation, with the powder, bullet, and every other circumstance as nearly Sect. III.

Practice nearly the same as possible, will yet range to very different distances.

5. The greatest part of that uncertainty in the ranges of pieces which is described in the preceding maxim, can only arise from the resistance of the air.

6. The resistance of the air acts upon projectiles in a twofold manner: for it opposes their motion, and by that means continually diminishes their velocity; and it besides diverts them from the regular track they would otherwise follow; whence arise those deviations and inflections already treated of.

7. That action of the air by which it retards the motion of projectiles, though much neglected by writers on artillery, is yet, in many instances, of an immense force; and hence the motion of these resisting bodies is totally different from what it would otherwise be.

8. This retarding force of the air acts with different degrees of violence, according as the projectile moves with a greater or lesser velocity; and the resistances observe this law. That to a velocity which is double another, the resistance within certain limits is fourfold; to a treble velocity, ninefold; and so on.

9. But this proportion between the resistances to two different velocities, does not hold if one of the velocities be less than that of 1200 feet in a second, and the other greater. For in that case the resistance to the greater velocity is near three times as much as it would come out by a comparison with the smaller, according to the law explained in the last maxim.

10. To the extraordinary power exerted by the resistance of the air it is owing, that when two pieces of different bores are discharged at the same elevation, the piece of the largest bore usually ranges farthest, provided they are both fired with fit bullets, and the customary allotment of powder.

11. The greatest part of military projectiles will at the time of their discharge acquire a whirling motion round their axis by rubbing against the inside of their respective pieces; and this whirling motion will cause them to strike the air very differently from what they would do had they no other than a progressive motion. By this means it will happen, that the resistance of the air will not always be directly opposed to their flight; but will frequently act in a line oblique to their course, and will thereby force them to deviate from the regular track they would otherwise describe. And this is the true cause of the irregularities described in maxim 4.

12. From the sudden trebling the quantity of the air's resistance, when the projectile moves swifter than at the rate of 1200 feet in a second (as hath been explained in maxim 9), it follows, that whatever be the regular range of a bullet discharged with this last mentioned velocity, that range will be but little increased how much ever the velocity of the bullet may be still farther augmented by greater charges of powder.

13. If the same piece of cannon be successively fired at an invariable elevation, but with various charges of powder, the greatest charge being the whole weight of the bullet in powder, and the least not less than the fifth part of that weight; then if the elevation be not less than eight or ten degrees, it will be found, that some of the ranges with the least charge will exceed some of those with the greatest.

14. If two pieces of cannon of the same bore, but of different lengths, are successively fired at the same elevation with the same charge of powder; then it will frequently happen, that some of the ranges with the shorter piece will exceed some of those with the longer.

15. In distant cannonadings, the advantages arising from long pieces and large charges of powder are but of little moment.

16. In firing against troops with grape-shot, it will be found, that charges of powder much less than those generally used are the most advantageous.

17. The principal operations in which large charges of powder appear to be more efficacious than small ones, are the ruining of parapets, the dismounting of batteries covered by stout merlons, or battering in breach; for, in all these cases, if the object be but little removed from the piece, every increase of velocity will increase the penetration of the bullet.

18. Whatever operations are to be performed by artillery, the least charges of powder with which they can be effected are always to be preferred.

19. Hence, then, the proper charge of any piece of artillery is not that allotment of powder which will communicate the greatest velocity to the bullet. (As most practitioners formerly maintained); nor is it to be determined by an invariable proportion of its weight to the weight of the ball; but, on the contrary, it is such a quantity of powder as will produce the least velocity for the purpose in hand; and, instead of bearing always a fixed ratio to the weight of the ball, it must be different according to the different business which is to be performed.

20. No field-piece ought at any time to be loaded with more than \( \frac{1}{3} \) or at the utmost \( \frac{1}{2} \) of the weight of its bullet in powder; nor should the charge of any battering piece exceed \( \frac{1}{2} \) of the weight of its bullet.

21. Although precepts very different from those we have here given have been often advanced by artillerymen, and have been said to be derived from experience; yet is that pretended experience altogether fallacious; since from our doctrine of resistance established above, it follows, that every speculation on the subject of artillery, which is only founded on the experimental ranges of bullets discharged with considerable velocities, is liable to great uncertainty.

The greatest irregularities in the motion of bullets are, as we have seen, owing to the whirling motion on their axis, acquired by the friction against the sides of rifled barrels. The best method hitherto known of preventing these is by the use of pieces with rifled barrels. These pieces have the insides of their cylinders cut with a number of spiral channels; so that it is in reality a female screw, varying from the common screws only in this, that its threads or rifles are less deflected, and approach more to a right line; it being usual for the threads with which the rifled barrel is indented, to take little more than one turn in its whole length. The numbers of these threads are different in each barrel, according to the size of the piece and the fancy of the workman; and in like manner the depth to which they are cut is not regulated by any invariable rule.

The usual method of charging these pieces is this: When the proper quantity of powder is put down, a leaden leaden bullet is taken, a small matter larger than the bore of the piece was before the rifles were cut; and this bullet being laid on the mouth of the piece, and consequently too large to go down of itself, it is forced by a strong rammer impelled by a mallet, and by repeated blows is driven home to the powder; and the softness of the lead giving way to the violence with which the bullet is impelled, that zone of the bullet which is contiguous to the piece varies its circular form, and takes the shape of the inside of the barrel; so that it becomes part of a male screw exactly answering to the indents of the rifle.

In some parts of Germany and Switzerland, however, an improvement is added to this practice; especially in the larger pieces which are used for shooting at great distances. This is done by cutting a piece of very thin leather, or of thin fustian, in a circular shape, somewhat larger than the bore of the barrel. This circle being greased on one side, is laid upon the muzzle with its greasy side downwards; and the bullet being then placed upon it, is forced down the barrel with it; by which means the leather or fustian incloses the lower half of the bullet, and, by its interposition between the bullet and the rifles, prevents the lead from being cut by them. But it must be remembered, that in the barrels where this is practised, the rifles are generally shallow, and the bullet ought not to be too large.—But as both these methods of charging at the mouth take up a good deal of time; the rifled barrels which have been made in Britain, are contrived to be charged at the breech, where the piece is for this purpose made larger than in any other part. The powder and bullet are put in through the side of the barrel by an opening, which, when the piece is loaded, is then filled up with a screw. By this means, when the piece is fired, the bullet is forced through the rifles, and acquires the spiral motion already described; and perhaps somewhat of this kind, says Mr Robins, though not in the manner now practised, would be of all others the most perfect method for the construction of these kinds of barrels.

From the whirling motion communicated by the rifles, it happens, that when the piece is fired, that indented zone of the bullet follows the sweep of the rifles; and thereby, besides its progressive motion, acquires a circular motion round the axis of the piece; which circular motion will be continued to the bullet after its separation from the piece; and thus a bullet discharged from a rifled barrel is constantly made to whirl round an axis which is coincident with the line of its flight. By this whirling on its axis, the aberration of the bullet which proves so prejudicial to all operations in gunnery, is almost totally prevented. The reason of this may be easily understood from considering the slow motion of an arrow through the air. For example, if a bent arrow, with its wings not placed in some degree in a spiral position, so as to make it revolve round its axis as it flies through the air, were shot at a mark with a true direction, it would constantly deviate from it, in consequence of being pressed to one side by the convex part opposing the air obliquely. Let us now suppose this deflection in a flight of 100 yards to be equal to 10 yards. Now, if the same bent arrow were made to revolve round its axis once every two yards of its flight, its greatest deviation would take place when it had proceeded only one yard, or made half a revolution; since at the end of the next half revolution it would again return to the same direction it had at first; the convex side of the arrow having been once in opposite positions. In this manner it would proceed during the whole course of its flight, constantly returning to the true path at the end of every two yards; and when it reached the mark, the greatest deflection to either side that could happen would be equal to what it makes in proceeding one yard, equal to \(\frac{1}{5}\)th part of the former, or 3.6 inches, a very small deflection when compared with the former one. In the same manner, a cannonball which turns not round its axis, deviates greatly from the true path, on account of the inequalities on its surface; which, although small, cause great deviations by reason of the resistance of the air, at the same time that the ball acquires a motion round its axis in some uncertain direction occasioned by the friction against its sides. But by the motion acquired from the rifles, the error is perpetually corrected in the manner just now described; and accordingly such pieces are much more to be depended on, and will do execution at a much greater distance, than the other.

The reasons commonly alleged for the superiority of rifle-barrels over common ones, are, either that the inflammation of the powder is greater, by the resistance which the bullet makes by being thus forced into the barrel, and that hereby it receives a much greater impulse; or that the bullet by the compounding of its circular and revolving motions, did as it were bore the air, and thereby flew to a much greater distance than it would otherwise have done; or that by the same boring motion it made its way through all solid substances, and penetrated into them much deeper than when fired in the common manner. But Mr Robins hath proved these reasons to be altogether erroneous, by a great number of experiments made with rifle-barrelled pieces. "In these experiments," says he, "I have found that the velocity of the bullet fired from a rifled barrel was usually less than that of the bullet fired from a common piece with the same proportion of powder. Indeed it is but reasonable to expect that this should be the case; for if the rifles are very deep, and the bullet is large enough to fill them up, the friction bears a very considerable proportion to the effort of the powder. And that in this case the friction is of consequence enough to have its effects observed, I have discovered by the continued use of the same barrel. For the metal of the barrel being lost, and wearing away apace, its bore by half a year's use was considerably enlarged, and consequently the depth of its rifles diminished; and then I found that the same quantity of powder would give to the bullet a velocity near a tenth part greater than what it had done at first. And as the velocity of the bullet is not increased by the use of rifled barrels, so neither is the distance to which it flies, nor the depth of its penetration into solid substances. Indeed these two last suppositions seem at first sight too chimerical to deserve a formal confutation. But I cannot help observing that those who have been habituated to the use of rifled pieces are very excusable in giving way to these prepossessions. For they constantly found, that with them they could fire at a mark with tolerable success, though it were placed at three or four times the distance to which the ordinary pieces were supposed to reach. And therefore, as they were ignorant of the true cause of this variety, and did not know that it arose only from preventing the deflection of the ball; it was not unnatural for them to imagine that the superiority of effect in the rifled piece was owing either to a more violent impulse at first, or to a more easy passage through the air.

In order to confirm the foregoing theory of rifle-barrelled pieces, I made some experiments by which it might be seen whether one side of the ball discharged from them uniformly keeps foremost during the whole course. To examine this particular, I took a rifled barrel carrying a bullet of six to the pound; but instead of its leaden bullet I used a wooden one of the same size, made of a soft springy wood, which bent itself easily into the rifles without breaking. And firing the piece thus loaded against a wall at such a distance as the bullet might not be shattered by the blow, I always found, that the same surface which lay foremost in the piece continued foremost without any sensible deflection during the time of its flight. And this was easily to be observed, by examining the bullet; as both the marks of the rifles, and the part that impinged on the wall, were sufficiently apparent. Now, as these wooden bullets were but the 16th part of the weight of the leaden ones; I conclude, that if there had been any unequal resistance or defective power, its effects must have been extremely sensible upon this light body, and consequently in none of the trials I made the surface which came foremost from the piece must have been turned round into another situation.

But again, I took the same piece, and, loading it now with a leaden ball, I set it nearly upright, sloping it only three or four degrees from the perpendicular in the direction of the wind; and firing it in this situation, the bullet generally continued about half a minute in the air, it rising by computation to near three quarters of a mile perpendicular height. In these trials I found that the bullet commonly came to the ground to the leeward of the piece, and at such a distance from it, as nearly corresponded to the angle of its inclination, and to the effort of the wind; it usually falling not nearer to the piece than 100, nor farther from it than 150 yards. And this is a strong confirmation of the almost steady flight of this bullet for about a mile and a half: for were the same trial made with a common piece, I doubt not but the deviation would often amount to half a mile, or perhaps considerably more; though this experiment would be a very difficult one to examine, on account of the little chance there would be of discovering where the ball fell.

It must be observed, however, that though the bullet impelled from a rifle-barrelled piece keeps for a time to its regular track with sufficient nicety; yet if its flight be so far extended that the track becomes considerably incurvated, it will then undergo considerable deflections. This, according to my experiments, arises from the angle at last made by the axis on which the bullet turns, and the direction in which it flies: for that axis continuing nearly parallel to itself, it must necessarily diverge from the line of the flight of the bullet, when that line is bent from its original direction; and when it once happens that the bullet whirls on an axis which no longer coincides with the line of its flight, then the unequal resistance formerly described will take place, and the deflecting power hence arising will perpetually increase as the track of the bullet, by having its range extended, becomes more and more incurvated.—This matter I have experienced in a small rifle-barrelled piece, carrying a leaden ball of near half an ounce weight. For this piece, charged with one drachm of powder, ranged about 550 yards at an angle of 12 degrees with sufficient regularity; but being afterwards elevated to an angle of 24 degrees, it then ranged very irregularly, generally deviating from the line of its direction to the left, and in one case not less than 100 yards. This apparently arose from the cause above mentioned, as was confirmed from the constant deviation of the bullet to the left; for by considering how the revolving motion was continued with the progressive one, it appeared that a deviation that way was to be expected.

The best remedy I can think of for this defect is the making use of bullets of an egg-like form instead of spherical ones. For if such a bullet hath its shorter axis made to fit the piece, and it be placed in the barrel with its smaller end downwards, then it will acquire by the rifles a rotation round its larger axis; and its centre of gravity lying nearer to its fore than its hinder part, its longer axis will be constantly forced by the resistance of the air into the line of its flight; as we see, that by the same means arrows constantly lie in the line of their direction, however that line be incurvated.

But, besides this, there is another circumstance in the use of these pieces, which renders the flight of their bullets uncertain when fired at a considerable elevation. For I find by my experiments, that the velocity of a bullet fired with the same quantity of powder from a rifled barrel, varies much more from itself in different trials than when fired from a common piece.—This, as I conceive, is owing to the great quantity of friction, and the impossibility of rendering it equal in each experiment. Indeed, if the rifles are not deeply cut, and if the bullet is nicely fitted to the piece, so as not to require a great force to drive it down, and if leather or fustian well greased is made use of between the bullet and barrel, perhaps, by a careful attention to all these particulars, great part of the inequality in the velocity of the bullet may be prevented, and the difficulty in question be in some measure obviated: but, till this be done, it cannot be doubted, that the range of the same piece, at an elevation, will vary considerably in every trial; although the charge be each time the same. And this I have myself experienced, in a number of diversified trials, with a rifle-barrelled piece loaded at the breech in the English manner. For here the rifles being indented very deep, and the bullet so large as to fill them up completely, I found, that though it flew with sufficient exactness to the distance of 400 or 500 yards; yet when it was raised to an angle of about 12 degrees (at which angle, being fired with one fifth of its weight in powder, its medium range is nearly 1000 yards); in this case, I say, I found that its range was variable, although the greatest care was taken to prevent any inequalities. inequalities in the quantity of powder, or in the manner of charging. And as, in this case, the angle was too small for the first-mentioned irregularity to produce the observed effects; they can only be imputed to the different velocities which the bullet each time received by the unequal action of the friction."

Thus we see, that it is in a manner impossible entirely to correct the aberrations arising from the resistance of the atmosphere; as even the rifle-barrelled pieces cannot be depended upon for more than one-half of their actual range at any considerable elevation. It becomes therefore a problem very difficult of solution to know, even within a very considerable distance, how far a piece will carry its ball with any probability of hitting its mark, or doing any execution. The best rules hitherto laid down on this subject are those of Mr Robins. The foundation of all his calculations is the velocity with which the bullet flies off from the mouth of the piece. Mr Robins himself had not opportunities of making many experiments on the velocities of cannon-balls, and the calculations from smaller ones cannot always be depended upon. In the 68th volume of the Phil. Trans. Mr Hutton hath recited a number of experiments made on cannon carrying balls from one to three pounds weight. His machine for discovering the velocities of these balls was the same with that of Mr Robins, only of a larger size. His charges of powder were two, four, and eight ounces; and the results of 15 experiments which seem to have been the most accurate, are as follow.

| Velocity with two ounces | Velocity with four ounces | Velocity with eight ounces | |-------------------------|--------------------------|---------------------------| | 702 feet in 1" | 1068 feet in 1" | 1419 feet in 1" | | 683 | 1020 | 1352 | | 695 | 948 | 1443 | | 703 | 973 | 1360 | | 725 | 957 | 1412 |

Mean velocities 701 993 1397

In another course, the mean velocities, with the same charges of powder, were 613, 873, 1162. "The mean velocities of the balls in the first course of experiments (says Mr Hutton) with two, four, and eight ounces of powder, are as the numbers 1, 1.414, and 1.993; but the subduplicate ratio of the weights (two, four, and eight) give the numbers 1, 1.414, and 2, to which the others are sufficiently near. - It is obvious, however, that the greatest difference lies in the last number, which answers to the greatest velocity. It will still be a little more in defect if we make the allowance for the weights of the balls; for the mean weights of the balls with the two and four ounces is 18.4 ounces, but of the eight ounces it is 18.5; diminishing therefore the number 1.993 in the reciprocal subduplicate ratio of 18.5 to 18.4, it becomes 1.985, which falls short of the number 2 by .015, or the 133rd part of itself. A similar defect was observed in the other course of experiments; and both are owing to three evident causes, viz. 1. The less length of cylinder through which the ball was impelled; for with the eight-ounce charge it lay three or four inches nearer to the muzzle of the piece than with the others. 2. The greater quantity of elastic fluid which escaped in this case than in the others by the windage. This happens from its moving with a greater velocity; in consequence of which, a greater quantity escapes by the vent and windage than in smaller velocities. 3. The greater quantity of powder blown out unfired in this case than in that of the lesser velocities; for the ball which was impelled with the greater velocity, would be sooner out of the piece than the others, and the more so as it had a less length of the bore to move through; and if powder fire in time, which cannot be denied, though indeed that time is manifestly very short, a greater quantity of it must remain unfired when the ball with the greater velocity issues from the piece, than when that which has the less velocity goes out, and still the more so as the bulk of powder which was at first to be inflamed in the one case so much exceeded that in the others.

"Let us now compare the corresponding velocities in both cases. In the one they are 701, 993, 1397; in the other, 613, 873, 1162. Now the ratio of the first two numbers, or the velocities with two ounces of powder, is that of 1 to 1.436, the ratio of the next two is that of 1 to 1.1375, and the ratio of the last is that of 1 to 1.2022. But the mean weight of the shot for two and four ounces of powder, was 28½ ounces in the first course and 18½ in this; and for eight ounces of powder, it was 28½ in the first and 18½ in this. Taking therefore the reciprocal subduplicate ratios of these weights of shot, we obtain the ratio of 1 to 1.224 for that of the balls which were fired with two ounces and four ounces of powder, and the ratio of 1 to 1.241 for the balls which were fired with eight ounces. But the real ratios above found are not greatly different from these; and the variation of the actual velocities from this law of the weights of shot, inclines the same way in both courses of experiments. We may now collect into one view the principal inferences that have resulted from these experiments.

1. "It is evident from them, that powder fires almost instantaneously.

2. "The velocities communicated to balls or shot of the same weight with different quantities of powder, are nearly in the subduplicate ratio of these quantities; a very small variation in defect taking place when the quantities of powder become great.

3. "When shot of different weights are fired with the same quantity of powder, the velocities communicated to them are nearly in the reciprocal subduplicate ratio of their weights.

4. "Shot which are of different weights, and impelled by 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."

The velocities of the bullets being thus found as nearly as possible, the ranges may be found by the following rules laid down by Mr Robins.

1. "Till the velocity of the projectile surpasses that of 1100 feet in a second, the resistance may be reckoned to be in the duplicate proportion of the velocity, and its mean quantity may be reckoned about half an ounce avoidupoise on a 12-pound shot, moving with a velocity of about 25 or 26 feet in a second.

2. "If the velocity be greater than that of 1100 or 1200 feet in a second, then the absolute quantity of the resistance in these greater velocities will be near three times as great as it should be by a comparison with..." Practice, with the smaller velocities.—Hence then it appears, that if a projectile begins to move with a velocity less than that of 1100 feet in 1', its whole motion may be supposed to be considered on the hypothesis of a resistance in the duplicate ratio of the velocity. And if it begins to move with a velocity greater than this last mentioned, yet if the first part of its motion, till its velocity be reduced to near 1100 feet in 1', be considered separately from the remaining part in which the velocity is less than 1100 feet in 1'; it is evident, that both parts may be truly assigned on the same hypothesis; only the absolute quantity of the resistance is three times greater in the first part than in the last. Therefore, if the motion of a projectile on the hypothesis of a resistance in the duplicate ratio of the velocity be truly and generally assigned, the actual motions of resisted bodies may be thereby determined, notwithstanding the increased resistances in the great velocities. And, to avoid the division of the motion into two, I shall show how to compute the whole at one operation with little more trouble than if no such increased resistance took place.

"To avoid frequent circumlocutions, the distance to which any projectile would range in a vacuum on the horizontal plain at 45° elevation, I shall call the potential range of that projectile; the distance to which the projectile would range in vacuo on the horizontal plane at any angle different from 45°, I shall call the potential range of the projectile at that angle; and the distance to which a projectile really ranges, I shall call its actual range.

"If the velocity with which a projectile begins to move is known, its potential range and its potential range at any given angle are easily determined from the common theory of projectiles*; or more generally, if either its original velocity, its potential range, or its potential range, at a given angle, are known, the other two are easily found out.

"To facilitate the computation of resisted bodies, it is necessary, in the consideration of each resisted body, to assign a certain quantity, which I shall denominate F, adapted to the resistance of that particular projectile. To find this quantity F to any projectile given, we may proceed thus: First find, from the principles already delivered, with what velocity the projectile must move, so that its resistance may be equal to its gravity. Then the height from whence a body must descend in a vacuum to acquire this velocity is the magnitude of F sought. But the simplest way of finding this quantity F to any shell or bullet is this: If it be of solid iron, multiply its diameter measured in inches by 300, the product will be the magnitude of F expressed in yards. If, instead of a solid iron-bullet, it is a shell or a bullet of some other substance; then, as the specific gravity of iron is to the specific gravity of the shell or bullet given, so is the F corresponding to an iron-bullet of the same diameter to the proper F for the shell or bullet given. The quantity F being thus assigned, the necessary computations of these resisted motions may be dispatched by the three following propositions, always remembering that these propositions proceed on the hypothesis of the resistance being in the duplicate proportion of the velocity of the resisted body. How to apply this principle, when the velocity is so great as to have its resistance augmented beyond this rate,

---

*See Projectile.

---

"PROP. I. Given the actual range of a given shell or bullet at any small angle not exceeding 8° or 10°, to determine its potential range, and consequently its potential range and original velocity.

"SOL. Let the actual range given be divided by the F corresponding to the given projectile, and find the quote in the first column of the preceding Table; then the corresponding number in the second column multiplied into F will be the potential range sought: and thence, by the methods already explained, the potential range and the original velocity of the projectile is given.

"Exam. An 18 pounder, the diameter of whose shot is about 5 inches, when loaded with 2 lb. of powder, ranged at an elevation of 3° 30' to the distance of 975 yards.

"The F corresponding to this bullet is 1500 yards, and the quote of the actual range by this number is 65; corresponding to which, in the second column, is .817; whence 817 F, or 1225 yards, is the potential range sought; and this, augmented in the ratio of the sine of twice the angle of elevation to the radius, gives..." gives 10050 yards for the potential range; whence it will be found, that the velocity of this projectile was that of 984 feet in a second.

"Cor. 1st. If the converse of this proposition be desired; that is, if the potential range in a small angle be given, and thence the actual range be sought; this may be solved with the same facility by the same table: for if the given potential range be divided by its correspondent F, then opposite to the quote sought in the second column, there will be found in the first column a number which multiplied into F will give the actual range required. And from hence it follows, that if the actual range be given at one angle, it may be found at every other angle not exceeding 8° or 10°.

"Cor. 2nd. If the actual range at a given small angle be given, and another actual range be given, to which the angle is sought; this will be determined by finding the potential ranges corresponding to the two given actual ranges; then the angle corresponding to one of these potential ranges being known, the angle corresponding to the other will be found by the common theory of projectiles.

"Cor. 3rd. If the potential range deduced from the actual range by this proposition exceeds 13000 yards; then the original velocity of the projectile was so great as to be affected by the treble resistance described above; and consequently the real potential range will be greater than what is here determined. However, in this case, the true potential range may be thus nearly assigned. Take a 4th continued proportional to 13000 yards, and the potential range found by this proposition, and the 4th proportional thus found may be assumed for the true potential range sought. In like manner, when the true potential range is given greater than 13000 yards, we must take two mean proportionals between 13000 and this range*; and the first of these mean proportionals must be assumed instead of the range given, in every operation described in these propositions and their corollaries. And this method will nearly allow for the increased resistance in large velocities, the difference only amounting to a few minutes in the angle of direction of the projected body, which, provided that angle exceeds two or three degrees, is usually scarce worth attending to.

Of this process take the following example.

"A 24 pounder fired with 12 pounds of powder, when elevated at 7° 15', ranged about 2500 yards. Here the F being near 1700 yards, the quote to be sought in the first column is 147, to which the number corresponding in the second column is 2556; whence the potential range is near 4350 yards, and the potential range thence resulting 17400. But this being more than 13000, we must, to get the true potential range, take a 4th continued proportional to 13000 and 17400; and this 4th proportional, which is about 31000 yards, is to be esteemed the true potential range sought; whence the velocity is nearly that of 1730 feet in a second.

"Scholium. This proposition is confined to small angles, not exceeding 8° or 10°. In all possible cases of practice, this approximation, thus limited, will not differ from the most rigorous solution by so much as what will often intervene from the variation of the density of the atmosphere in a few hours time; so that the errors of the approximation are much short of other inevitable errors, which arise from the nature of this subject.

"PROP. II. Given the actual range of a given shell or bullet, at any angle not exceeding 45°, to determine its potential range at the same angle; and thence its potential range and original velocity.

"Sol. Diminish the F corresponding to the shell or bullet given in the proportion of the radius to the cosine of \( \frac{1}{4} \) of the angle of elevation. Then, by means of the preceding table, operate with this reduced F in the same manner as is prescribed in the solution of the last proposition, and the result will be the potential range sought; whence the potential range, and the original velocity, are easily determined.

"Exam. A mortar for sea-service, charged with 30lb. of powder, has sometimes thrown its shell, of 12½ inches diameter, and of 231 lb. weight, to the distance of 2 miles, or 5450 yards. This at an elevation of 45°.

"The F to this shell, if it were solid, is 3825 yards; but as the shell is only \( \frac{1}{4} \) of a solid globe, the true F is no more than 3060 yards. This, diminished in the ratio of the radius to the cosine of \( \frac{1}{4} \) of the angle of elevation, becomes 2544. The quote of the potential range by this diminished F is 1384; which sought in the first column of the preceding table gives 2280 for the corresponding number in the second column; and this multiplied into the reduced F, produces 5800 yards for the potential range sought, which, as the angle of elevation was 45°, is also the potential range; and hence the original velocity of this shell appears to be that of about 748 feet in a second.

"Cor. The converse of this proposition, that is, the determination of the actual range from the potential range given, is easily deduced from hence by means of the quote of the potential range divided by the reduced F; for this quote searched out in the second column will give a corresponding number in the first column, which multiplied into the reduced F, will be the actual range sought.

"Also, if the potential range of a projectile be given, or its actual range at a given angle of elevation; its actual range at any other angle of elevation, not greater than 45°, may hence be known. For the potential range will assign the potential range at any given angle; and thence, by the method of this corollary, the actual range may be found.

"Exam. A fit musket-bullet fired from a piece of the standard dimensions, with \( \frac{1}{4} \) of its weight in good powder, acquires a velocity of near 900 feet in a second; that is, it has a potential range of near 8400 yards. If now the actual range of this bullet at 15° was sought, we must proceed thus:

"From the given potential range it follows, that the potential range at 15° is 4200 yards; the diameter of the bullet is \( \frac{1}{4} \) of an inch; and thence, as it is of lead, its proper F is 337.5 yards, which, reduced in the ratio of the radius to the cosine of \( \frac{1}{4} \) of 15°, becomes 331 yards. The quote of 4200 by this number is 12.7 nearly; which, being sought in the second column, gives 3.2 nearly for the corresponding number in the first column; and this multiplied into 331 yards (the reduced F) makes 1059 yards for the actual range sought.

"Exam. II. The same bullet, fired with its whole weight in powder, acquires a velocity of about 2100 feet." Practice feet in a second, to which there corresponds a potential random of about 45700 yards. But this number greatly exceeding 13000 yards, it must be reduced by the method described in the third corollary of the first proposition, when it becomes 19700 yards. If now the actual range of this bullet at 15° was required, we shall from hence find, that the potential range at 15° is 9850 yards, which, divided by the reduced F of the last example, gives for a quote 2975; and thence following the steps prescribed above, the actual range of this bullet comes out 1396 yards, exceeding the former range by no more than 337 yards; whereas the difference between the two potential ranges is above ten miles. Of such prodigious efficacy is the resistance of the air, which hath been hitherto treated as too insignificant a power to be attended to in laying down the theory of projectiles!

"SCHOL. I must here observe, that as the density of the atmosphere perpetually varies, increasing and diminishing often by \( \frac{1}{10} \) part, and sometimes more, in a few hours; for that reason I have not been over rigorous in forming these rules, but have considered them as sufficiently exact when the errors of the approximation do not exceed the inequalities which would take place by a change of \( \frac{1}{10} \) part in the density of the atmosphere. With this restriction, the rules of this proposition may be safely applied in all possible cases of practice. That is to say, they will exhibit the true motions of all kinds of shells and cannon-shot, as far as 45° of elevation, and of all musket bullets fired with their largest customary charges, if not elevated more than 30°. Indeed, if experiments are made with extraordinary quantities of powder, producing potential randoms greatly surpassing the usual rate; then in large angles some farther modifications may be necessary. And though, as these cases are beyond the limits of all practice, it may be thought unnecessary to consider them; yet, to enable those who are so disposed to examine these uncommon cases, I shall here insert a proposition, which will determine the actual motion of a projectile at 45°, how enormous forever its original velocity may be. But as this proposition will rather relate to speculative than practical cases, instead of supposing the actual range known, thence to assign the potential random, I shall now suppose the potential random given, and the actual range to be thence investigated.

"PROP. III. Given the potential random of a given shell or bullet, to determine its actual range at 45°.

Sol. Divide the given potential random by the F corresponding to the shell or bullet given, and call the quotient q, and let l be the difference between the tabular logarithms of 25 and of q, the logarithm of 10 being supposed unity; then the actual range sought is

\[ 3.4F + \frac{11}{10}Fq \]

where the double sine of \( 2lF \) is to be thus understood; that if q be less than 25, it must be \( -2lF \); if it be greater, then it must be \( +2lF \). In this solution, q may be any number not less than 3, nor more than 2500.

"Cor. Computing in the manner here laid down, we shall find the relation between the potential randoms, and the actual range at 45°, within the limits of this proposition, to be as expressed in the following table.

| Potential Random | Actual Range at 45° | |------------------|---------------------| | 3 F | 1.5 F | | 6 F | 2.1 F | | 10 F | 2.6 F | | 20 F | 3.2 F | | 30 F | 3.6 F | | 40 F | 3.8 F | | 50 F | 4.0 F | | 100 F | 4.6 F | | 200 F | 5.1 F | | 500 F | 5.8 F | | 1000 F | 6.4 F | | 2500 F | 7.0 F |

Whence it appears, that, when the potential random is increased from 3 F to 2500 F, the actual range is only increased from 1.5 F to 7 F; so that an increase of 2497 F in the potential random produces no greater an increase in the actual range than 5.5 F, which is not its \( \frac{1}{4} \) part; and this will again be greatly diminished on account of the increased resistance, which takes place in great velocities. So extraordinary are the effects of this resistance, which we have been hitherto taught to regard as inconsiderable.

"That the justness of the approximations laid down in the 2d and 3d propositions may be easier examined; I shall conclude these computations by inserting a table of the actual ranges at 45° of a projectile, which is raised in the duplicate proportion of its velocity. This table is computed by methods different from those hitherto described, and is sufficiently exact to serve as a standard with which the result of our other rules may be compared. And since whatever errors occur in the application of the preceding propositions, they will be most sensible at 45° of elevation, it follows, that hereby the utmost limits of those errors may be assigned.

| Potential Randoms | Actual Range at 45° | |-------------------|---------------------| | 1 F | 0.963 F | | 2.5 F | 1.282 F | | 5 F | 1.420 F | | 7.5 F | 1.586 F | | 10 F | 1.732 F | | 12.5 F | 1.860 F | | 15 F | 1.978 F | | 17.5 F | 2.083 F | | 20 F | 1.179 F | | 22.5 F | 1.349 F | | 30 F | 1.495 F | | 35 F | 1.624 F | | 40 F | 1.738 F | | 45 F | 1.840 F | | 50 F | 1.930 F | | 55 F | 2.015 F | | 60 F | 2.097 F | | 65 F | 2.169 F | | 70 F | 2.237 F | | 75 F | 2.300 F | | 80 F | 2.359 F | | 85 F | 2.414 F | | 90 F | 2.467 F | | 95 F | 2.511 F | | 100 F | 2.564 F | | 110 F | 2.651 F |

Vol. VIII. Part I.

Practice.

Potential Randoms. Actual Range at 45°.

| Calib | Length | Weight | |-------|--------|--------| | 3 | 4 | 6 | | | 7 | 1 | | | 7 | 1 |

| Calib | Length | Weight | |-------|--------|--------| | 3 | 3 | 3 | | | 3 | 3 |

Of the different parts and proportions of guns.

We have now only to consider that part of practical gunnery which relates to the proportions of the different parts of cannon, the metal of which they are made, &c.

Formerly the guns were made of a very great length, and were on that account extremely troublesome and unmanageable. The error here was first discovered by accident; for some cannon, having been cast by mistake two feet and an half shorter than the common standard, were found to be equally efficacious in service with the common ones, and much more manageable. This soon produced very considerable alterations in the form of the artillery throughout Europe; but in no country have greater improvements in this respect been made than in our own. For a long time brass, or rather a kind of bell-metal, was thought preferable to cast iron for making of cannon. The composition of this metal is generally kept a secret by each particular founder.

The author of the Military Dictionary gives the following proportions as the most common, viz. "To 240 lb. of metal fit for casting they put 68 lb. of copper, 52 lb. of brass, and 12 lb. of tin. To 4200 lb. of metal fit for casting the Germans put 3687½ lb. of copper, 2042½ lb. of brass, and 307½ lb. of tin. Others use 100 lb. of copper, 6 lb. of brass, and 9 lb. of tin; while some make use of 100 lb. of copper, 10 lb. of brass, and 15 lb. of tin. This composition was both found to be very expensive, and also liable to great inconveniences in the using. A few years ago, therefore, a proposal was made by Mr Muller for using iron guns of a lighter construction than the brass ones, by which he supposed that a very great saving would be made in the expense; and likewise, that the guns of the new construction would be more manageable, and even efficacious, than the old ones. "The reduction of the expense (says Mr Muller) of the very large artillery necessary for sea and land service, is to be considered under two heads: the one, To diminish the weight; and the other, Not to use any brass field-artillery, but only iron, to lessen the great burden of our ships of war, and to carry larger calibers than those of other nations of the same rate. If the weights of our guns are diminished, they will require fewer hands to manage them, and of consequence a smaller number will be exposed to danger at a time: and if we carry larger calibers, our rates will be a match for larger ships.

"The advantage of using iron guns in the field instead of brass, will be that the expenses are lessened in proportion to the cost of brass to that of iron, which is as 8 to 1.

"The only objection against iron is, its pretended brittleness: but as we abound in iron that is stronger and tougher than any brass, this objection is invalid. This I can affirm; having seen some that cannot be broken by any force, and will flatten like hammered iron: if then we use such iron, there can be no danger of the guns bursting in the most severe action.

"Though brass guns are not liable to burst, yet they are sooner rendered unferviceable in action than iron. For by the softness of the metal, the vent widens too soon, and they are so liable to bend at the muzzle, that it would be dangerous to fire them; as we found by experience at Belleisle, and where we were obliged to take guns from the ships to finish the siege.

"These being undeniable facts, no possible reason can be assigned against using iron guns in both sea and land service, and thereby lessen the expenses of artillery so considerably as will appear by the following tables.

Lengths and Weights of Iron Ship-Guns.

| Old Pieces | New Pieces | |------------|-----------| | Calib | Length | Weight | Calib | Length | Weight | | Ft. In. | Ft. In. | | 3 | 4 | 6 | 3 | 3 | 3 | | | 7 | 1 | | 3 | 3 | | | 7 | 1 | | 3 | 3 |

"Guns of this construction appear sufficiently strong from the proof of two three-pounders made for Lord Egmont, and they even may be made lighter and of equal service.

Length and Weight of Battering Pieces.

| Old Brass | New Iron | |-----------|----------| | Calib | Length | Weight | Calib | Length | Weight | | Ft. In. | Ft. In. | | 6 | 8 | 19 | 1 | 6 | 19 | | | 9 | 25 | 0 | 9 | 14 | | | 9 | 29 | 0 | 12 | 8 | | | 9 | 6 | 48 | 0 | 18 | 9 | | | 9 | 6 | 51 | 0 | 24 | 8 | | | 10 | 0 | 55 | 2 | 32 | 9 |

Total 227. Total 151. Diff. 72.

"That these guns are sufficiently strong, is evident from the former trial; besides, there are several 32 pounders of the same dimensions and weight now existing and serviceable; though cast in king Charles II.'s time.

N. B. N.B. These battering pieces may serve in garrisons.

"It appears from these tables, that no proportion has been observed in any guns hitherto made, in respect to their length or weight, but merely by guess.

Some Examples to show what may be saved by this Scheme.

The old Royal George carried 100 brass guns, which weighed together 218.2 tons; the ton costs 130 pounds, workmanship included.

The expense of these guns is then 28366 pounds

A set of iron guns of the same number and calibers, according to my construction, weighs 127.8 tons

The ton costs 16 pounds, and the whole set 2044.8 pounds

The Royal George carries then 90.4 tons more than is necessary, and the difference between the expense is 26321.2 pounds

That is, 12.5 times more than the new iron set costs; or 12 ships of the same rate may be fitted out at less charge.

A set of the Old iron guns for a New first-rate weighs 127.8 tons

The difference between the weight of the old and new is 76.6 tons

The difference between the expense is then 1225.6 pounds

A set of brass battering pieces weighs 11.36 tons

A ton costs 130 pounds, and the set 1476.8 pounds

A set of the new weighs 7.55 tons

The ton costs 16 pounds, and the set 117.8 pounds

That is, the old set costs 11 times, and 632 over, more than the new set; or 11 sets of the new could be made at less expense than one of the old.

"This table shows what may be saved in the navy; and if we add those on board sloops, the different garrisons, and the field train, with the great expense of their carriage in the field, it may be found pretty near as much more."

| Num of Guns | Weight of Old | Weight of New | Diff. | Num of Shps | Total Difference | |-------------|---------------|---------------|------|-------------|-----------------| | 100 | 4367 3 | 2556 0 | 1811 | 3 | 90578 0 | | 90 | 3537 3 | 2001 0 | 1536 | 9 | 13827 3 | | 80 | 3108 3 | 1827 0 | 1287 | 3 | 9014 1 | | 74 | 1091 0 | 1840 2 | 1250 | 2 | 30016 0 | | 70 | 2997 0 | 1796 2 | 1200 | 2 | 12005 0 | | 64 | 2543 3 | 1305 0 | 1258 | 2 | 28485 2 | | 62 | 2177 3 | 1185 0 | 972 | 3 | 29782 2 | | 50 | 1881 1 | 1035 0 | 846 | 1 | 16078 3 | | 44 | 1365 2 | 705 0 | 660 | 2 | 5284 0 | | 40 | 1234 2 | 312 2 | 922 | 9 | 8298 0 | | 36 | 963 3 | 450 0 | 513 | 3 | 3596 1 | | 32 | 956 2 | 435 0 | 521 | 2 | 14602 0 | | 28 | 593 2 | 285 0 | 308 | 2 | 7095 1 | | 24 | 581 3 | 255 0 | 276 | 3 | 3321 0 | | 20 | 421 2 | 191 0 | 230 | 1 | 4353 3 |

Difference between the weights - 201918 3

Expenses of the Brass guns of two first rates - 203918 14

We get L. 157028 0

This and other proposals for reducing the weight and expense of guns have been greatly attended to of late; and the Carron company in Scotland have not only greatly improved those of the old construction, but a gun of a new construction hath been invented by Mr Charles Galcogues director of that work, which promises to be of more effectual service than any hitherto made use of.—Fig. 6. represents the form and proportions of the guns made at Carron, and which serve for those of all sizes, from ½ pounders of the guns and upwards. The proportions are measured by the made at diameters of the caliber, or bore of the gun, divided Carron, into 16 equal parts, as represented in the figure.

The following are the names of the different parts of a cannon.

AB, the length of the cannon. AE, the first reinforce. EF, the second reinforce. FB, the chase. HB, the muzzle. Ao, the cascabel, or pomiglion. AC, the breech. CD, the vent-field. FI, the chase-girdle. rr, the base-ring and ogee. t, the vent-alfragal and fillets. Pq, the first reinforce-ring and ogee. vw, the second reinforce ring and ogee. x, the chase-alfragal and fillets. z, the muzzle-alfragal and fillets. n, the muzzle mouldings. m, the dwelling of the muzzle. Ai, the breech mouldings. TT, the trunnions.

The dotted lines along the middle of the piece show the dimensions of the caliber, and the dotted circle shows the size of the ball. Fig. 7. shows a cannon made also at Carron, and which may be measured by the same scale.

As the breech of the cannon receives an equal impulse with the bullet from the action of the inflamed explosion of gunpowder, it thence follows, that at the moment the bullet flies off, the piece itself pushes backward with very great force. This is called the recoil of the cannon; and if the piece is not of a very considerable weight, it would fly upwards, or to a side, with extreme violence. If again it was firmly fastened down, so that it could not move in the least, it would be very apt to burst, on account of the extreme violence with which the powder would then act upon it. For this reason it hath been found necessary to allow the recoil to take place, and consequently all large pieces of artillery are mounted upon carriages with wheels, which allow them to recoil freely; and thus they may be fired without any danger. There are several sorts of carriages for ordnance, viz. bastard carriages, with low wheels and high wheels; sea-carriages, made in imitation of those for ship-guns; and carriages for field-pieces, of which there are two kinds. The carriages must be proportioned to the pieces mounted on them. The ordinary proportion is for the carriage to have once and a half the length of the gun, the wheels to be half the length of the piece in height. Four times the diameter or caliber gives the depth of the planks in the fore end; in the middle 3½. Fig. 8. shows Mr Gascoigne's newly-invented or rather improved gun called a carronade*; and which, in June 1779, was by the king and council instituted a standard navy-gun, and 10 of them appointed to be added to each ship of war, from a first-rate to a sloop. Of this gun the Carron company have published the following account.

"The carronade is made so short, that it is worked with its carriage in the ship's port; the trunnions lying immediately over the fill of the port: it is correctly bored; and the shot being perfectly round, fills the caliber with such exactness, that the least possible of the impulse of the powder escapes, upon explosion, between the cylinder and the shot; which last also is thereby more truly directed in its flight. The bottom of the cylinder is a hemisphere, to which the end of the cartridge is not liable to stick, and in which the smallest charge of powder envelopes the shot, exhausting nearly the whole of its impelling force upon it: the trunnions are placed so as to lessen the recoil, and that the gun cannot rest against the sides of the carriage, and is balanced with the utmost facility. There are views cast upon the vent and muzzle, to point the gun quickly to an object at 250 and 500 yards distance. There is an handle A fixed upon the pommel-end of the gun, by which it is horizontally ranged and pointed; and there is a ring cast upon the cabcab, through which the breechin rope is reeved, the only rope used about these guns.

"The carronade is mounted upon a carriage B, with a perfectly smooth bottom of strong plank, without trucks; instead of which there is fixed on the bottom of the carriage, perpendicular from the trunnions, a gudgeon C of proper strength, with an iron washer D and pin E at the lower end thereof. This gudgeon is let into a corresponding groove F, cut in a second carriage G, called a slide-carriage; the washer supported by the pin over reaching the under-edges of the groove H. This slide-carriage is made with a smooth upper surface, upon which the gun-carriage is moved, and by the gudgeon always kept in its right station to the port; the groove in the slide-carriage being of a sufficient length to allow the gun to recoil and be loaded within board. The slide-carriage, the groove included, is equally broad with the fore-part of the gun-carriage, and about four times the length; the fore-part of the slide-carriage is fixed by hinge-bolts I, to the quick-work of the ship below the port, the end lying over the fill, close to the outside plank, and the groove reaching to the fore end; the gudgeon of the gun-carriage, and consequently the trunnions of the gun, are over the fill of the port when the gun is run out; and the port is made of such breadth, with its sides bevelled off within board, that the gun and carriage may range from bow to quarter. The slide-carriage is supported from the deck at the hinder end, by a wedge K, or step-stool; which being altered at pleasure, and the fore-end turning upon the hinge-bolts, the carriage can be constantly kept upon an horizontal plane, for the more easy and quick working of the gun when the ship lies along.

"The gun and carriages being in their places, the breechin rope, which must be strong and limber, is reeved through the ring on the breech, then led thro' an eye-bolt drove downwards, the eye standing up-right upon the upper edge of each cheek of the gun-carriage; from these eye-bolts the ends of the breechin rope are seized down as usual to an eye bolt driven into the quick-work on each side, in a line with the lower surface of the slide-carriage.

"The gun being mounted and ready for action, is loaded with \(\frac{1}{4}\)th part of the weight of its ball in service charge of powder put into a woollen cartridge, and the end tied up with a worsted yarn, and placed next to the shot; and with a single ball, well rammed home upon the powder, without a wadding between them: the gun being then run out in the port, is ranged and elevated with great facility, by means of the handle on the pommel; and, by the views, very quickly pointed.—Upon discharge, the gun attempts to kick upwards, which being prevented by the washer of the gudgeon bearing hard against the under part of the slide-carriage, the recoil takes place; and the gudgeon sliding backwards in the groove (the washer still bearing against an iron plate on the under edge of the groove); till the gun is brought up by the breechin rope, as much re-action succeeds as slackens the rope, so that the gun and carriage may be instantly turned fore and aft by the handle, and loaded again.

"This gun has many singular advantages over the others of light construction.—It is so extremely light, that the smallest ships can carry almost any weight of shot (the 12-pounder weighing under 500 wt. and the other calibers in proportion), and that without being attended with the inconveniences imputed generally to light guns, since it cannot injure its carriage, or jump out of its station in the port upon recoil; and it will never heat.

"It can be easily managed and worked of all calibers, from the 12 pounders downwards with two hands, and the 18 and 24-pounders with three hands. It may be readily ranged, pointed, and discharged, twice in three minutes, which doubles the strength of the ship against an enemy of equal force. It is wrought upon an horizontal plane to windward or to leeward—how much ever the ship lies along under a pressure of sail; and therefore, besides being hampered with no tackles or other ropes, except the breechin rope, it may be worked with as much ease and expedition in chase or in a gale of wind as in lying to for action.—It can be ranged from bow to quarter, so as to bring a broadside to bear in a circuit of above 10 points of the compass on each side.—It is no more expensive in ammunition than the old guns of two-thirds less weight of shot; and it requires very few hands above the complement necessary for navigating merchant-ships; and increases the strength of privateers crews, by exposing few hands at the guns, and augmenting the number at small arms.

"Though the carronade cannot, strictly speaking, throw its shot to an equal distance with a longer gun; yet, from the fitness of the shot to its cylinder, the powers of this gun will greatly surpass the expectations of such as are not intimately acquainted with the effects of the elastic force of fired powder, since, with \(\frac{1}{4}\)th part of the weight of its ball, at very small elevations, it will range its shot to triple the distance which ships generally engage, with sufficient velocity for the greatest execution, and with all the accuracy in its..." its direction that can be attained from guns of greater lengths.

"There have been two seeming disadvantages imputed to this gun, which it does not merit, viz. the nicety of fitting the shot to the bore of the gun, and its incapacity to hold more than two shot at one charge. But as seamen have few opportunities of confirming themselves in just opinions by experiments made on shore, and cannot, in that case, be fully conversant with the subject; the following loose hints may not be inept towards removing these objections.

"It is an axiom in projectiles, That a shot cannot be impelled from a gun to any distance in a direction truly parallel to the axis of the cylinder of the piece, or what is commonly called point-blank, arising from several well-known causes: for, however just may be the cylinder, and however perfect and smooth may be the sphere of its corresponding shot, and admitting that the impulse of the powder acts through the centre of gravity of the shot, and also that the shot consequently leaves the piece in a direction parallel to the axis of its cylinder; yet is the shot no sooner discharged, but it becomes more or less inflected by its gravity, and deflected, according to its velocity, by the reflexion of the air and wind.

"These irregularities are of little importance in close sea-fights, and, being the effect of natural causes, are common to all. Besides these, the deviation of a shot from its true direction, is further augmented by the windage between the cylinder and its shot; but the greatest uncertainty in the flight of a shot, making allowance for the action of its gravity, and the air's resistance, springs from the defects of the shot itself. Round-shot for ship-guns are seldom nicely examined; and, unless they are cast solid and truly globular, and free of all hollows, roughnesses, and other outside blemishes, and well fitted to the gun, it cannot even be discharged in the direction of the axis of the piece; to the disappointment of those that use such, and to the discredit of the gun-founder, however justly the piece is viewed, or disparted; but, being impelled against the surface of the cylinder, bounds and rebounds from side to side, acquires a rotatory motion, and when cast hollow withal, and breaking within the cylinder before discharge, (which sometimes happens, especially with double charges), never fails to injure; and, when often repeated, may at last burst the very best guns.—Round-shot should not be taken on board a ship, without being examined as to its shape and surface, gaged for its size to the caliber of the gun, and weighed that it be not above or below the standard more than half an ounce in the pound of its respective caliber: good shot then, being of the same importance to all guns, removes the first objection.

"If the direction of the flight of a shot to its object is affected by so many seeming trivial causes, how much more uncertain must it be, when two or more shot are discharged together from one gun? for the shot next the powder being impelled with more celerity than that immediately before it, strikes against it after discharge, and sometimes shivers itself to pieces, and never fails to change obliquely the direction of both; and this happens with round and double-headed, &c., and all double charges; and which, from their various figures, cannot reach an object at the same elevations with the round-shot; especially when these other shots are of greater weight than the round, which is often the case. However frightful a broadside with double charges may appear at sea, more confusion is created by them, and more time lost, within board, by the strain and excessive recoil, than real damage done without board by the additional charge: for upon a trial on shore, where the effect can be traced, it will be found, that, at 100 yards distance, more shot will take place within a small compass by single than by double charges; and the charges will be oftener repeated in a given time, without heating the gun: and these facts being established, remove also the second objection."

The following account of the proof of one of these guns will perhaps serve to give a more adequate idea of the great usefulness of them, than any description:

"On Monday, Oct. 4, 1779, there was an experiment made at Carron, before the earl of Dunmore, &c. &c. with a 68 pounder carronade, nearly of the weight of a British navy 12-pounder gun, and charged with the same quantity (viz. 6 lb.) of powder.—The carronade was mounted, on its proper carriages, into a port of the dimensions of a 74 gun ship's lower-deck port; was pointed without elevation, at a centre of eight inches diameter, marked on a bulk's head of the thickness of two feet five inches solid wood, at 163 yards distance; behind which, at 168 yards, there was another bulk's head of two feet four inches thick; and behind that again, at 170 yards distance, a bank of earth. The shot pierced the bulk's heads each time, and was buried from three to four feet into the bank; and the splinters were thrown about to a considerable distance on all sides.

| Shot | Distance Below Horizontal Line | Distance from Mark | |------|--------------------------------|-------------------| | 1st | 1 foot 7 inches | 5 feet | | 2nd | 2 feet | ditto | | 3rd | do. through the horizontal line | ditto | | 4th | do. | ditto | | 5th | do. | ditto | | 6th | 2 inches below | ditto | | 7th | do. touched the lower part of ditto | ditto | | 8th | 2 inches below | ditto | | 9th | 2 feet below | ditto | | 10th | 3 inches below | ditto |

"The Carronade was laid each time by the views without an instrument; and the shot were all to the left of the mark, owing to a small error in dispersing the views; the third, fourth, and fifth shot, made one fracture, as did also sixth, seventh, and eighth, and the fifth and eighth struck the same spot.

"The Carronade was easily worked with four men, and may be readily worked and discharged on board a..." We have already seen of how much consequence rifle-barrels are in order to bring the art of gunnery to perfection; as they enlarge the space in which the ball will fly without any lateral deflection to three or four times its usual quantity. This improvement, however, till very lately, only took place in musket-barrels. But in the beginning of the year 1774, Dr Lind, and Captain Alexander Blair of the 69th regiment of foot, invented a species of rifled field-pieces. They are made of cast iron; and are not bored like the common pieces, but have the rifles moulded on the core, after which they are cleaned out and finished with proper instruments.

Guns of this construction, which are intended for the field, ought never to be made to carry a ball of above one or two pounds weight at most; a leaden bullet of that weight being sufficient to destroy either man or horse.—A pound-gun, of this construction, of good metal, such as is now made by the Carron company, need not weigh above an hundred pounds weight, and its carriage about another hundred. It can, therefore, be easily transported from place to place, by a few men; and a couple of good horses may transport six of these guns and their carriages, if put into a cart.

But, for making experiments, in order to determine the resistance which bodies moving with great velocities meet with from the air, a circumstance to which these guns are particularly well adapted, or for annoying an enemy's fappers that are carrying on their approaches towards a beleaguered place, a larger caliber may be used.

The length of the gun being divided into seven equal parts, the length of the first reinforce AB is two of these parts; the second BC, one and \( \frac{1}{2} \) of the diameter of the caliber; the chase CD, four wanting \( \frac{1}{2} \) of the diameter of the caliber.

The distance from the hind-part of the base-ring A to the beginning of the bore, is one caliber and \( \frac{1}{2} \) of a caliber. The trunnions TT are each a caliber in breadth, and the same in length; their centres are placed three-sevenths of the gun's length from the hind part of the base ring, in such a manner that the axis of the trunnions passes through the centre line of the bore, which prevents the gun from kicking, and breaking its carriage. The length of the caulkable is one caliber and \( \frac{1}{2} \) of a caliber.

The caliber of the gun being divided into 16 equal parts;

The thickness of metal at the base-ring A from the bore, is

At the end of the first reinforce ring B

At the same place, for the beginning of the second reinforce

At the end of the second reinforce C

At the same place, for the beginning of the chase c

At the end of the chase or muzzle, the mouldings a D excluded

At the swelling of the muzzle b

At the muzzle-fillet c

At the extreme moulding D

The bullets, fig. 10, are of lead, having six knobs cast on them to fit the rifles of the gun. Being thus made of soft metal, they do not injure the rifles; and may also save an army the trouble of carrying a great quantity of shot about with them, since a supply of lead... Practice. Lead may be had in most countries from reefs, &c., which can be cast into balls as occasion requires. Lead likewise being of greater specific gravity than cast-iron, flies to a much greater distance.

Rifled ordnance of any caliber might be made to carry iron shot, for battering or for other purposes; provided holes, that are a little wider at their bottoms than at their upper parts, be cast in a zone round the ball, for receiving afterwards leaden knobs to fit the rifles of the cannon; by which means, the iron shot will have its intended line of direction preserved, without injuring the rifles more than if the whole ball was of lead, the rotatory motion round its axis, in the line of its direction (which corrects the aberration) being communicated to it by the leaden knobs, following the spiral turn of the rifles in its progress out of the gun.

It is particularly to be observed, that the balls must be made to go easily down into the piece, so that the cartridge with the powder and the bullet may be both sent home together, with a single push of the hand, without any wadding above either powder or ball; by which means, the gun is quickly loaded, and the ball flies farther than when it is forcibly driven into the gun, as was found from many experiments. The only reason why, in common rifled muskets, the bullets are rammed in forcibly, is this, that the zone of the ball which is contiguous to the inside of the bore may have the figure of the rifles impressed upon it, in such a manner as to become part of a male screw, exactly fitting the indents of the rifle, which is not at all necessary in the present case, the figure of the rifles being originally cast upon the ball. These knobs retard the flight of the bullet in some degree; but this small disadvantage is fully made up by the ease with which the gun is loaded, its service being nearly as quick as that of a common field-piece; and the retardation and quantity of the whirling motion which is communicated to the bullet being constantly the same, it will not in the least affect the experiments made with them, in order to determine the resistance of the air.

In order to hit the mark with greater certainty than can be done in the common random method, these guns are furnished with a sector, the principal parts of which are, 1. The limb, which is divided in such a manner as to show elevations to 15 or 20 degrees. The length of the radius is five inches and an half, and its nonius is so divided as to show minutes of a degree. 2. The telescope, AB, fig. 11, an achromatic refractor, is seven inches in length (such as is used on Hadley's quadrants, that are fitted for taking distances of the moon from the sun or stars, in order to obtain the longitude at sea), having cross hairs in it. 3. The parallel cylindrical bar, CD, is \( \frac{3}{4} \) of an inch in diameter, having two rectangular ends EF, each half an inch square and an inch long. On one side of the end next the limb of the sector, is a mark corresponding to a similar one in the hinder cock of the gun, with which it must always coincide when placed on the gun. The length of the parallel bar, together with its ends, is seven inches. This bar is fixed to the sector by means of two hollow cylinders, G, H, which allow the sector a motion round the bar. There is a finger-screw, a, upon the hollow cylinder G, which is slit, in order to tighten it at pleasure upon the bar. 4. The circular level I, fig. 11, and 12, for setting the plane of the sector always perpendicular when placed upon the gun, is \( \frac{1}{4} \) of an inch in diameter. There is a small screw, d, to adjust the level at right angles to the plane of the sector. 5. The finger-screw, b, for fixing the index of the sector at any particular degree of elevation proposed.

The line of collimation (that is, the line of vision cut by the intersecting point of the two cross-hairs in the telescope) must be adjusted truly parallel to the bar of the sector when at 0 degrees. This is done by placing the sector so that the vertical hair may exactly cover some very distant perpendicular line. If it again covers it when the sector is inverted, by turning it half round upon the bar, which has all the while been kept steady and firm, that hair is correct; if not, correct half the error by means of the small screws, c, d, e, fig. 11. and 13, at the eye-end of the telescope, and the other half by moving the bar; place it again to cover the perpendicular line, and repeat the above operation till the hair covers it in both positions of the sector. Then turn the sector, till the horizontal hair covers the same perpendicular line; and turning the sector half round on its bar, correct it, if wrong, in the same manner as you did the vertical hair.

N.B. Of the four small screws at the eye-end of the telescope, those at the right and left hand move whatever hair is vertical, and those at top or underneath move whatever hair is horizontal.

On the side of the gun upon the first reinforce, are cast two knobs, F, fig. 9. and 14, having their middle part distant from each other six inches, for fixing on the brass cocks, A, fig. 14. and 15, which receive the rectangular ends of the parallel cylindrical bar of the sector, when placed on the gun.

The next adjustment is to make the parallel bar, and line of collimation of the telescope, when set at 0 degrees, parallel to the bore of the gun, and consequently to the direction of the shot. The gun being loaded, the cartridge pricked, and the gun primed, place the sector in the cocks of the gun; and having first set the sector to what elevation you judge necessary, bring the intersection of the cross hairs in the telescope upon the centre of the mark, the limb of the sector being set vertical by means of the circular level, and then take off the sector without moving the gun. Fire the gun; and if the bullet hits anywhere in the perpendicular line, passing through the centre of the mark, the line of collimation of the telescope and direction of the shot agree. But if it hit to the right of the mark, so much do they differ. In order to correct which, bring the gun into the same position it was in before firing, and secure it there. Then file away as much of the fore-cock, on the side next the gun, as will let the intersection of the cross-hair fall somewhere on the line passing perpendicularly through the point where the shot fell; and it is then adjusted in that position, so much being filed off the side of the cock at a, fig. 14. and 18, as will allow the side b to be screwed closer, that the ends of the parallel bar may have no shake in the cocks. To correct it in the other position, and so to find the true 0 degrees of the gun, that is, to bring the line of collimation of the telescope, parallel-bar, and bore of the gun, truly parallel to each other, repeat the above with the trunnions perpendicular to the horizon, the sector being turned a quarter round upon its bar. bar, so as to bring its plane vertical. The deviation of the shot found in this way is corrected by deepening one of the cocks, so that the vertical hair of the telescope may be brought to cover the line passing perpendicularly through the point where the bullet hits; the gun being placed in the same position it was in before it was fired. This adjustment being repeated two or three times, and any error that remains being corrected, the gun is fit to be mounted on its carriage for service. It is to be observed, that this sector will fit any gun, if the cocks and rectangular ends, &c. of the parallel bar be of the above dimensions, and will be equally applicable to all such pieces whose cocks have been adjusted, as if it had been adjusted separately with each of them. And if the sector be set at any degree of elevation, and the gun moved so as to bring the intersection of the cross-hairs on the object to be fired at (the limb of the sector being vertical), the bore of the gun will have the same elevation above it, in the true direction of the shot, whatever position the carriage of the gun is standing in. A telescope with cross hairs, fixed to a common rifled musket, and adjusted to the direction of the shot, will make any person, with a very little practice, hit an object with more precision than the most experienced marksman.

For garrison-service, or for batteries, the ship or garrison carriage, with two iron staples on each side to put through a couple of poles to carry these guns from place to place with more dispatch, are as proper as any. But, for the field, a carriage like that at fig. 16, where the shafts push in upon taking out the iron pins ab, and moving the cross bar A, upon which the breech of the gun rests, as far down as the shafts were pushed in, is the properest, since the whole can then be carried like a hand-barrow, over ditches, walls, or rough ground, all which may be easily understood from the figure.

The principal advantage that will accrue from the use of rifled ordnance, is the great certainty with which any object may be hit when fired at with them, since the shot deviates but little from its intended line of direction, and the gun is capable of being brought to bear upon the object, with great exactness, by means of the telescope and cross-hairs.

The other pieces of artillery commonly made use of are mortars, howitzers, and royals. The mortars are a kind of short cannon of a large bore, with chambers for the powder, and are made of brass or iron. Their use is to throw hollow shells filled with powder, which falling on any building, or into the works of a fortification, burst, and with their fragments destroy every thing near them. Carcasses are also thrown out of them; which are a sort of shells with five holes, filled with pitch and other materials, in order to set buildings on fire; and sometimes baskets full of stones, of the size of a man's fist, are thrown out of them upon an enemy placed in the covert-way in the time of a siege. Of late the ingenious General Delaguiers has contrived to throw bags filled with grape-shot, containing in each bag from 400 to 600 shot of different dimensions, out of mortars. The effect of these is tremendous to troops forming the line of battle, passing a defile, or landing, &c. the shot pouring down like a shower of hail on a circumference of above 300 feet.

Mortars are chiefly distinguished by the dimensions of their bore; for example, a 13th-inch mortar is one the diameter of whose bore is 13 inches, &c.—The land-mortars are those used in sieges, and of late in battles. They are mounted on beds, and both mortar and bed are transported on block carriages. There is likewise a kind of land-mortars mounted on travelling carriages, invented by count Buckeburg, which may be elevated to any degree; whereas all the English mortars are fixed to an angle of 45°. This custom, however, does not appear to have any foundation in reason. In a siege, shells should never be thrown with an angle of 45 degrees, excepting one case only; that is, when the battery is so far off, that they cannot otherwise reach the works; for when shells are thrown out of the trenches into the works of a fortification, or from the town into the trenches, they should have as little elevation as possible, in order not to bury themselves, but to roll along the ground, whereby they do much more damage, and occasion a much greater consternation among the troops, than if they sunk into the ground. On the contrary, when shells are thrown upon magazines, or any other buildings, the mortars should be elevated as high as possible, that the shells may acquire a greater force in their fall, and consequently do more execution.

There are other kinds of mortars, called partridge-mortars, hand-mortars, and firelock-mortars; which last are also called bombards. The partridge-mortar is a common one, surrounded with 13 other little mortars bored round its circumference, in the body of the metal; the middle one is loaded with a shell, and the others with grenades. The vent of the large mortar being fired, communicates its fire to the rest; so that both the shell and grenades go off at once. Hand-mortars were frequently used before the invention of coehorns. They were fixed at the end of a staff four feet and a half long, the other end being fitted with iron to stick in the ground; and while the bombardier with one hand elevated it at pleasure, he fired it with the other. The firelock-mortars, or bombards, are small mortars fixed to the end of a firelock. They are loaded as all common firelocks are; and the grenade, placed in the mortar at the end of the barrel, is discharged by a flint-lock. To prevent the recoil hurting the bombardier, the bombard rests on a kind of halberd made for that purpose.

The chamber in mortars is the place where the powder is lodged. They are of different forms, and made variously by different nations; but the cylindric seems to be preferable to any other form.

The howitz is a kind of mortar mounted on a field-carriage like a gun: it differs from the common mortars in having the trunnions in the middle, whereas those of the mortar are at the end. The construction of howitzes is as various and uncertain as that of mortars, excepting that the chambers are all cylindric. They are distinguished by the diameter of their bore; for instance, a 10-inch howitz is that which has a bore of 10 inches diameter, and so of others. They were much more lately invented than mortars, and indeed are plainly derived from them.

Royals Royals are a kind of small mortars, which carry a shell whose diameter is 5.5 inches. They are mounted on beds in the same way as other mortars.

Fig. 17 represents a mortar; and the names of its parts are as follow:

- **A B**, the whole length of the mortar. - **AC**, the muzzle. - **CD**, chace. - **DE**, reinforce. - **EF**, breech. - **GH**, trunnions. - **a**, vent. - **b**, dolphin. - **c d**, vent-aftragal and fillets. - **d e**, breech-ring and ogee. - **f g**, reinforce-ring and ogee. - **g h**, reinforce-aftragal and fillets. - **i k**, muzzle-aftragal and fillets. - **k l**, muzzle-ring and ogee. - **l m**, muzzle mouldings. - **n**, shoulders.

**Interior parts.** - **o**, chamber. - **p**, bore. - **q**, mouth. - **r**, vent.

The mortar-beds are formed of very solid timber, and placed upon very strong wooden frames, fixed in such a manner that the bed may turn round. The fore-part of these beds is an arc of a circle described from the centre on which the whole turns.

There are several instruments employed in the loading of cannon. The names of these are as follow:

1. The lantern or ladle, which serves to carry the powder into the piece, and which consists of two parts, viz., of a wooden box, appropriated to the caliber of the piece for which it is intended, and of a caliber and a half in length with its vent; and of a piece of copper nailed to the box, at the height of a half caliber.—This lantern must have three calibers and a half in length, and two calibers in breadth, being rounded at the end to load the ordinary pieces.

2. The rammer is a round piece of wood, commonly called a box, fastened to a stick 12 feet long, for the pieces from 12 to 33 pounds; and 10 for the 8 and 4-pounders; which serve to drive home the powder and ball to the breech.

3. The sponge is a long staff or rammer, with a piece of flannel or lamb-skin wound about its end, to serve for scouring the cannon when discharged, before it be charged with fresh powder; to prevent any spark of fire from remaining in her, which would endanger the life of him who should load her again.

4. Wad-screw consists of two points of iron turned serpent-wise, to extract the wad out of the pieces when one wants to unload them, or the dirt which had chanced to enter into it.

5. The botefeuks are sticks two or three feet long, and an inch thick, split at one end, to hold an end of the match twisted round it, to fire the cannon.

6. The priming-iron is a pointed iron-rod, to clear the touch-hole of the pieces of powder or dirt; and also to pierce the cartridge, that it may sooner take fire.

7. The primer, which must contain a pound of powder at least, to prime the pieces.

8. The quoin of mire, which are pieces of wood with a notch on the side to put the fingers on, to draw them back or push them forward when the gunner points his piece. They are placed on the sole of the carriage.

9. Leaden-plates, which are used to cover the touch-hole, when the piece is charged, lest some dirt should enter it and stop it.

Before charging the piece, it is well sponged, to clean it of all filth and dirt within itself; then the proper weight of gunpowder is put in and rammed down; care being taken that the powder be not bruised in ramming, which weakens its effect; it is then run over by a little quantity of paper, hay, or the like; and lastly, the ball is thrown in.

To point, level, or direct the piece, so as to play against any certain point, is done by the help of a quadrant with a plummet; which quadrant consists of two branches made of braids or wood; one about a foot long, eight lines broad, and one line in thickness; the other four inches long, and the same thickness and breadth as the former. Between these branches is a quadrant, divided into 90 degrees, beginning from the shorter branch, and furnished with thread and plummet.

The longest branch of this instrument is placed in the cannon’s mouth, and elevated or lowered till the thread cuts the degree necessary to hit the proposed object. Which done, the cannon is primed, and then set fire to. The method by the sector, however, proposed by Dr Lind, is certainly in all cases to be preferred.

A 24-pounder may very well fire 90 or 100 shots every day in summer, and 60 or 75 in winter. In case of necessity it may fire more; and some French officers of artillery assure, that they have caused such a piece to fire every day 150 shots in a siege.—A 16 and a 12-pounder fire a little more, because they are easier served. There have even been some occasions where 200 shots have been fired from these pieces in the space of nine hours, and 138 in the space of five. In quick firing, tubes are made use of. They are made of tin; and their diameter is two-tenths of an inch, being just sufficient to enter into the vent of the piece. They are about six inches long, with a cap above, and cut slanting below, in the form of a pen; the point is strengthened with some folder, that it may pierce the cartridge without bending. Through this tube is drawn a quick-match, the cap being fitted with mealed powder moistened with spirits of wine. To prevent the mealed powder from falling out by carriage, a cap of paper or flannel steeped in spirits of wine is tied over it. To range pieces in a battery, care must be taken to reconnoitre well the ground where it is to be placed, and the avenues to it. The pieces must be armed each with two lanterns or ladles, a rammer, a sponge, and two priming-irons. The battery must also be provided with carriages, and other implements, necessary to remount the pieces which the enemy should chance to dismount.

To serve expeditiously and safely a piece in a battery, it is necessary to have to each a sack of leather, large large enough to contain about 20 pounds of powder to charge the lanterns or ladles, without carrying them to the magazine; and to avoid thereby making those trains of powder in bringing back the lantern from the magazine, and the accidents which frequently happen thereby.

A battery of three pieces must have 30 gabions, because six are employed on each of the two sides or epaulets, which make 12, and nine for each of the two merlons.

There ought to be two gunners and six soldiers to each piece, and an officer of artillery.

The gunner posted on the right of the piece must take care to have always a pouch full of powder and two priming irons; his office is to prime the piece, and load it with powder. The gunner on the left fetches the powder from the little magazine, and fills the lantern or ladle which his comrade holds; after which, he takes care that the match be very well lighted, and ready to set fire to the piece at the first command of the officer.

There are three soldiers on the right and three on the left of the piece. The two first take care to ram and sponge the piece, each on his side. The rammer and sponge are placed on the left, and the lantern or ladle on the right. After having rammed well the wad put over the powder and that put over the bullet, they then take each a handspike, which they pass between the foremost spokes of the wheel, the ends whereof will pass under the head of the carriage, to make the wheel turn round, leaning on the other end of the handspike, towards the embrasure.

It is the office of the second soldier on the right to provide wad, and to put it into the piece, as well over the powder as over the bullet; and that of his comrade on the left to provide 50 bullets, and every time the piece is to be charged to fetch one of them and put it into the piece after the powder has been rammed. Then they both take each an handspike, which they pass under the hind part of the wheel, to push it in battery.

The officer of artillery must take care to have the piece diligently served.

In the night he must employ the gunners and soldiers, who shall relieve those who have served 24 hours to repair the embrasures.

If there be no water near the battery, care must be taken to have a cask filled with it, in which to dip the sponges and cool the pieces every 10 or 12 rounds.

The carriage for a mortar of 12 inches of diameter must be 6 feet long, the flasks 12 inches long and 10 thick. The trunions are placed in the middle of the carriage.

The carriage of an 18 inch mortar must be 4 feet long, and the flasks 11 inches high and 6 thick.

To mount the mortars of new invention, they use carriages of cast iron.

In Germany, to mount mortars from 8 to 9 inches, and carry them into the field, and execute them horizontally as a piece of cannon, they make use of a piece of wood 8 feet 2 inches long, with a hole in the middle to lodge the body of the mortar and its trunions as far as their half diameter, and mounted on two wheels four feet high, to which they join a vantrain proportioned to it, and made like those which serve to the carriages of cannons.

Having mounted the mortar on its carriage, the next thing is to calibrate the bomb by means of a great caliber, the two branches whereof embrace the whole circumference of the bomb: these two branches are brought on a rule where the different calibers are marked, among which that of the bomb is found.

If no defect be found in the bomb, its cavity is filled, by means of a funnel, with whole gunpowder; a little space or liberty is left, that when a fusee or wooden tube, of the figure of a truncated cone, is driven through the aperture (with a wooden mallet, not an iron one for fear of accident), and fastened with a cement made of quicklime, ashes, brick dust, and steel filings, worked together in a glutinous water, or of four parts of pitch, two of colophony, one of turpentine, and one of wax, the powder may not be bruised. This tube is filled with a combustible matter made of two ounces of nitre, one of sulphur, and three or more of gunpowder dust well rammed. See Fuzee.

This fusee set on fire burns slowly till it reaches the gunpowder; which goes off at once, bursting the shell to pieces with incredible violence. Special care, however, must be taken that the fusee be so proportioned as that the gunpowder do not take fire ere the shell arrives at the destined place; to prevent which, the fusee is frequently wound round with a wet clammy thread.

Batteries consist—1. Of an epauletment to shelter the mortars from the fire of the enemy. 2. Of platforms on which the mortars are placed. 3. Of small magazines of powder. 4. Of a boyau, which leads to the great magazine. 5. Of ways which lead from the battery to the magazine of bombs. 6. Of a great ditch before the epauletment. 7. Of a berm or retrace.

The platforms for mortars of 12 inches must have 9 feet in length and 6 in breadth.—The lambourds for common mortars must be four inches thick; those of a concave chamber of 8 lb. of powder, 5 inches; those of 12 lb. 6 inches; those of 18 lb. 7 inches or thereabouts. Their length is at discretion, provided there be enough to make the platforms 9 feet long.—The forepart of the platform will be situated at two feet distance from the epauletment of the battery.—The bombardiers, to shelter themselves in their battery, and not be seen from the town besieged, raise an epauletment of 7 feet or more high, which epauletment has no embrasures.

To serve expeditiously a mortar in battery, there are required,—five strong handspikes; a dame or rammer, of the caliber of the conic chamber, to ram the wad and the earth; a wooden knife a foot long, to place the earth round the bomb; an iron scraper two feet long, one end whereof must be four inches broad and round-wise, to clean the bore and the chamber of the mortar, and the other end made in form of a spoon to clean the little chamber; a kind of brancard to carry the bomb, a shovel, and pick-axe.

The officer who is to mind the service of the mortar must have a quadrant to give the degrees of elevation.

Five bombardiers, or others, are employed in that service; the first must take care to fetch the powder to charge the chamber of the mortar, putting his priming-iron in the touch-hole before he charges the chamber; and never going to fetch the powder before he has asked his officer at what quantity of powder he designs to charge, because more or less powder is wanted according to the distance where it is fired; the same will take care to ram the wad and earth, which another soldier puts in the chamber.

The soldier on the right will put again two shovelful of earth in the bottom of the bore, which should be likewise very well rammed down.

This done, the rammer or dame is returned into its place against the epaulet on the right of the mortar; he takes an handspike in the same place to post himself behind the carriage of the mortar, in order to help to push it into battery; having laid down his handspike, he takes out his priming-iron, and primes the touch-hole with fine powder.

The second soldier on the right and left will have by that time brought the bomb ready loaded, which must be received into the mortar by the first soldier, and placed very strait in the bore or chafe of the mortar.

The first on the right will furnish him with earth to put round the bomb, which he must take care to ram close with the knife given him by the second on the left.

This done, each shall take a handspike, which the two first on the right and left shall put under the pegs of retreat of the forepart, and the two behind under those of the hindpart, and they together push the mortar in battery.

Afterwards the officer points or directs the mortar.

During that time the first soldier takes care to prime the touch-hole of the mortar, without ramming the powder; and the last on the right must have the match ready to set fire to the fusee of the bomb on the right, while the first is ready with his on the left to set fire to the touch-hole of the mortar, which he ought not to do till he sees the fusee well lighted.

The foremost soldiers will have their handspikes ready to raise the mortar upright as soon as it has discharged, while the hindmost on the left shall with the scraper clean the bore and chamber of the mortar.

The magazine of powder for the service of the battery shall be situated 15 or 20 paces behind, and covered with boards and earth over it.—The loaded bombs are on the side of the said magazine, at five or six paces distance.

The officer who commands the service of the mortar must take care to discover as much as possible with the eye the distance of the place where he intends to throw his bomb, giving the mortar the degree of elevation according to the judgment he has formed of the distance. Having thrown the first bomb, he must diminish or increase the degrees of elevation according to the place upon which it shall fall. Several make use of tables to discover the different distances according to the differences of the elevations of the mortar, especially the degrees of the quadrant from 1 to 45°; but these, from the principles already laid down, must be fallacious.

The petard is the next piece of artillery which deserves our attention; and is a kind of engine of metal, somewhat in shape of a high-crowned hat, serving to break down gates, barricades, draw-bridges, or the like works, which are intended to be surprized. It is very short, narrow at the breech and wide at the muzzle, made of copper mixed with a little brass, or of lead with tin.

The petards are not always of the same height and bigness: they are commonly 10 inches high, 7 inches of diameter a-top, and 10 inches at bottom. They weigh commonly 40, 45, and 50 pounds.

The madrier, on which the petard is placed, and where it is tied with iron circles, is of two feet for its greatest width, and of 18 inches on the sides, and no thicker than a common madrier. Under the madrier are two iron-bars paffed crosswise, with a hook, which serves to fix the petard.

To charge a petard 15 inches high, and 6 or 7 inches of caliber or diameter at the bore, the inside must be first very well cleaned and heated, so that the hand may bear the heat; then take the best powder that may be found, throw over it some spirit of wine, and expose it to the sun, or put it in a frying-pan; and when it is well dried, 5 lb. or 6 lb. of this powder is put into the petard, which reaches within three fingers of the mouth; the vacancies are filled with tow, and stopped with a wooden tampon; the mouth being strongly bound up with cloth tied very tight with ropes; then it is fixed on the madrier, that has a cavity cut in it to receive the mouth of the petard, and fastened down with ropes.

Some, instead of gunpowder for the charge, use one of the following composition, viz. gunpowder seven pounds, mercury sublimate one ounce, camphor eight ounces; or gunpowder six pounds, mercury sublimate three ounces, and sulphur three; or gunpowder six, beaten glass half an ounce, and camphor three quarters.

Before any of these pieces are appropriated for service, it is necessary to have each undergo a particular trial of its soundness, which is called a proof, to be made by or before one authorized for the purpose, called the proof-master.

To make a proof of the piece, a proper place is chosen, which is to be terminated by a mound of earth very thick to receive the bullets fired against it, that none of them may run through it. The piece is laid on the ground, supported only in the middle by a block of wood. It is fired three times; the first with powder of the weight of the bullet, and the two others with \( \frac{1}{3} \) of the weight; after which a little more powder is put in to singe the piece; and after this, water, which is impressed with a sponge, putting the finger on the touch-hole to discover if there be any cracks; which done, they are examined with the cat, which is a piece of iron with three grasps, disposed in the form of a triangle, and of the caliber of the piece; then it is visited with a wax-candle, but it is of very little service in the small pieces, because if they be a little long the smoke extinguishes it immediately. See Plate CCXXIV.

Besides the large pieces already mentioned, invented for the destruction of mankind, there are others called arms, small guns; viz. muskets of ramparts, common muskets, fusils, carbines, muletoons, and pistols.

A musket, or musquet, is a fire-arm borne on the shoulder, and used in war, formerly fired by the application of a lighted match, but at present with a flint and lock. The common musket is of the caliber of 20 leaden balls to the pound, and receives balls from 22 to 24; its length is fixed to 3 feet 8 inches from the muzzle to the touch-pan. A fusil, or fire-lock, has the same length and caliber, and serves at present instead of a musket.

A carbine is a small fort of fire-arm, shorter than a fusil, and carrying a ball of 24 in the pound, borne by the light-horse, hanging at a belt over the left shoulder. This piece is a kind of medium between the pistol and the musket; and bears a near affinity to the arquebus, only that its bore is smaller. It was formerly made with a match-lock, but of late only with a flint-lock.

The musquetoon is of the same length of the carbine, the barrel polished, and clean within. It carries five ounces of iron, or seven and a half of lead, with an equal quantity of powder.

The barrel of a pittol is generally 14 inches long.

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