ftions hence arifing; and many difputes on motion Thery were fet on foot (especially in Italy), which continued till the time of Galileo, and probably gave rife to his celebrated Dialogues on motion. These were publifhed 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 irreconcileable with the motions of thefe bodies. Very few of the ancients indeed refrained from indulging themselves in fpeculations concerning the difference betwixt natural, violent, and mixed motions; although scarce any two of them could agree in their theories.

Theory of larger pieces, is yet fufficiently adapted to the ftrength of the ufual profiles of fortification; and that the facility of their carriage and management, and the ammunition they fpare, give them great advantages beyond the whole cannons formerly employed in making breaches. The method alfo of making a breach, by first cutting off the whole wall as low as poffible before its upper part is attempted to be beat down, feems alfo to be a confiderable modern improvement in the practical part of gunnery. But the moft confiderable improvement in the practice is the method of firing with fmall quantities of powder, and elevating the piece fo 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 fmall angle, and with a small velocity, does not bury itfelf, 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 filence, or the front it is to fweep, each fhot rakes the whole length of that battery or front; and has thereby a much greater chance of difabling the defendants, and difmounting their cannon, than it would have if fired in the common manner. This method was invented by Vauban, and was by him ftyled Batterie à Ricochet. It was first put in practice in the year 1692 at the fiege of Aeth.-Something fimilar to this was put in practice by the king of Pruffia at the battle of Rofbach in 1757. He had feveral fixinch mortars, made with trunnions and mounted on travelling carriages, which fired obliquely on the enemy's lines, and amongst their horfe. They were charged with eight ounces of powder, and elevated at an angle of one degree fifteen minutes, and did great execution; for the fhells rolling along the lines with burning-fufes made the stouteft of the enemy not wait for their burfting.

Theory of gunnery first at

Tartalea.

SECT. II. Theory of Gunnery.

THE ufe of fire-arms had been known for a long time before any theory concerning them was at tempted. The first author who wrote profeffedly on tempted by the flight of cannon-fhot was Tartalea. In 1537 he published a book, at Venice, intitled Nova Scientia; and afterwards another, intitled Quafiti et Inventioni diverfi, printed at the fame place in 1546, in which he treats profeffedly on thefe motions. His difcoveries were but few, on account of the imperfect ftate of mechanical knowledge at that time. However, he determined, that the greatest range of cannon was with an elevation of 45 degrees. He likewife 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 fome cafes fo little, that it was not attended to. He compared it to the furface of the fea; which, though it appears to be a plane, is yet undoubtedly incurvated round the centre of the earth. He also affumes to himself the invention of the gunner's quadrant, and often gave fhrewd gueffes at the event of fome untried methods. But as he had not opportunities of being converfant in the practice, and founded his opinions only on fpeculation, he was condemned by most of the fucceeding writers, though often without any fufficient reafon. The philofophers of thofe times alfo intermeddled in the que

differe

It is ftrange, however, that, during all thefe con- Experi tefts, fo few of those who were intrusted with the meats by charge of artillery thought it worth while to bring these theories to the test of experiment. Mr Robins the rang informs us, in his Preface to the New Principles of of arulis, Gunnery, that he had met with no more than four authors who had treated on this fubject. The first of these is Collado, who has given the ranges of a falconet carrying a three-pound fhot to each point of the gunner's quadrant. But from his numbers it is manifeft, that the piece was not charged with its cuftomary allotment of gun-powder. The refults of his trials were, that the point-blank fhot, 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 7° 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 fix, 1053 paces. At the fe venth point, the range fell between thofe of the third and fourth; at the eighth point, it fell between the ranges of the fecond and third; at the ninth point, it fell between the ranges of the first and fecond; at the tenth point, it fell between the point-blank diftance 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 treatife, another appeared on the fame fubject by one Bourne an Englishman. His elevations were not regulated by the points of the gunner's quadrant, but by degrees; and he afcertains the proportions between the ranges at different elevations and the extent of point-black fhot. According to him, if the extent of the point-blank fhot be reprefented by 1, the range at 50 elevation will be 23, at 10° it will be 34, at 15° it will be 4, at 20° it will be 4%, and the greatest random will be 5. This laft, he tells us, is in a calm day when the piece is elevated to 42°; but according to the ftrength of the wind, and as it favours or opposes the flight of the fhot, 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 fmall 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 den. fity of the bullet.

After him Eldred and Anderfon, both Englishmen, publifhed treatifes on this fubject. The firft pub

Theory. lished his treatife in 1646, and has given the actual ranges of different pieces of artillery at fmall elevations all under ten degrees. His principles were not rigoroufly true, though not liable to very confiderable errors; yet, in confequence of their deviation from the truth, he found it impoffible to make fome of his experiments agree with his principles.

alileo's eory.

5

y by Anerfon.

In 1638, Galileo printed his dialogues on motion. In these he pointed out the general laws obferved by nature in the production and compofition of motion; and was the first who defcribed the action and effects of gravity on falling bodies. On the fe principles he determined, that the flight of a cannon fhot, or any other projectile, would be in the curve of a parabola, except in as far as it was diverted from that track by the resistance of the air. He has alfo propofed the means of examining the inequalities which arife from thence, and of discovering what fenfible effects that refiftance would produce in the motion of a bullet at fome given distance from the piece.

Though Galileo had thus fhown, that, independent of the refiftance of the air, all projectiles would, in their flight, defcribe the curve of a parabola; yet those who came after him, feem never to have imagined that it was necessary to confider how far the operations of gunnery were affected by this refiftance. The fubfequent writers indeed boldly afferted, without making the experiment, that no confiderable variation could arife from the refiftance of the air in the flight of fhells or cannon fhot. In this perfuafion they fupported themselves chiefly by confidering the extreme rarity of the air, compared with those denfe and ponderous bodies; and at laft it become an almoft generally established maxim, that the flight of these bodies was nearly in the curve of a parabola.

In 1674, Mr Anderson above-mentioned publishNew theo ed his treatise on the nature and effects of the gun; in which he proceeds on the principles of Galileo, and ftrenuously afferts, that the flight of all bullets is in the curve of a parabola; undertaking to anfwer all objections that could be brought to the contrary. The fame thing was also undertaken by Mr Blondel, in a treatise published at Paris in 1683; where, after long difcuffion, the author concludes, that the variations from the air's refiftance are fo flight as scarce to merit notice. The fame subject is treated of in the Philofophical Tranfactions, N° 216. p. 68. by Dr Halley; and he alfo, fwayed by the very great difproportion between the denfity of the air and that of iron or lead, thinks it reasonable to believe, that the oppofition of the air to large metal-fhot is fcarcely difcernible; although in small and light shot he owns that it must be accounted for.

But though this hypothefis went on fmoothly in fpeculation; yet Anderson, who made a great number of trials, found it impoffible to support it without fome new modification. For though it does not appear that he ever examined the comparative ranges of either cannon or musket hot when fired with their ufual velocities, yet his experiments on the ranges of fhells thrown with small velocities (in comparison of thofe above-mentioned), convinced him that their whole tract was not parabolical. But inftead of making the proper inferences from hence, and concluding the refiftance of the air to be of confiderable efficacy, he

framed a new hypothefis; which was, that the fhell or Theory. bullet, at its firft difcharge, flew to a certain diftance in a right line, from the end of which line only it began to defcribe a parabola. And this right line, which he calls the line of the impulfe of the fire, he fuppofes to be the fame in all elevations. Thus, by affigning a proper length to this line of impulfe, it was always in his power to reconcile any two fhots made at different angles, let them differ as widely as we please to fuppofe. But this he could not have done with three fhots; nor indeed doth he ever tell us the event of his experiments when three ranges were tried at one time.

6

the air's re

When Sir Ifaac Newton's Principia was published, Laws of he particularly confidered the refiftance of the air to fiftance laid. projectiles which moved with small velocities; but as down by he never had an opportunity of making experiments Newton. on those which move with fuch prodigious fwiftness, he did not imagine that a difference in velocity could make fuch differences in the refiftance as are now found to take place. Sir Ifaac found, that, in fmail velocities, the refiitance was increafed in the duplicate proportion of the fwiftness 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 refiftance as the firft, with thrice the velocity it would meet with nine times the refiftance, &c.-This prin- Erroneous ciple itfelf is now found to be erroneous with regard to in military military projectiles; though, if it had been properly projectiles attended to, the refiftance of the air might even from thence have been reckoned much more confiderable than was commonly done. So far, however, were those who treated this fubject feientifically, from giving a proper allowance for the refiftance of the atmofphere, that their theories differed most egregiously from the truth. Huygens alone feems to have attended to this principle: for, in the year 1690, he published a treatife on Gravity, in which he gave an account of fome experiments tending to prove, that the track of all projectiles moving with very fwift motions was widely different from that of a parabola. All the rest of the learned acquiefced in the juftnefs 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 offi. All these cer of artillery, diftinguished by the number of fieges widely dif at which he had ferved, by his high military rank, and ferent from by his abilities in his profeffion, gave in a memoir to the truth. the Royal Academy, of which he was a member, importing, that," although it was agreed, that theory joined with practice did conftitute the perfection of every art; yet experience had taught him, that theory was of very little fervice in the ufe of mortars: That the works of M. Blondel had juftly enough defcribed the feveral 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 precifion, to point a mortar agreeably to thefe calculations, he had never been able to eftablish any folid foundation upon them."

From the history of the academy, it doth not appear that the fentiments of Mr Reffons were at any time controverted, or any reafon offered for the failure of

the

8

theories

Theory. the theory of projectiles when applied to ufe. Nothing farther, however, was done till the time of Benjamin Robins, who in 1742 published a treatife, intitled, Mr Robins New Principles of Gunnery, in which he hath treated first intro. particularly not only of the refiftance of the atmoduces a true fphere, but almost every thing elfe relating to the flight theory. of military projectiles, and indeed advanced the theory of gunnery much nearer perfection than ever it was

ΤΟ

His method

der.

before.

The first thing confidered by Mr Robins, and which of determi is indeed the foundation of all other particulars relaning the tive to gunnery, is the explofive force of gunpowder. force of This he determined to be owing to an elaftic fluid fi gunpow. milar to our atmosphere, having its elaftic force greatly increased by the heat. "If a red-hot iron (fays he) be included in a receiver, and the receiver be exhaufted, and gunpowder be then let fall on the iron, the powder will take fire, and the mercurial gage will fuddenly defcend upon the explosion; and though it immediately afcends again, it will never rife to the height it firft ftood at, but will continue depreffed by a space proportioned to the quantity of powder which was let fall on the iron.-The fame production likewife takes place when gunpowder is fired in the air: for if a small quantity of powder is placed in the upper part of a glafs tube, the lower part of which is immerfed in water, and the fluid be made to rife so near the top, that only a small portion of air is left in that part where the gunpowder is placed; if in this fituation 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-glafs, the water will in this experiment defcend on the explosion, as the quickfilver did in the laft; and will always continue depreffed below the place at which it flood before the explosion. The quantity of this depreffion will be greater if the quantity of powder be increased, or the diameter of the tube be diminished.

"When any confiderable quantity of gunpowder is fired in an exhausted receiver, by being let fall on a red-hot iron, the mercurial gage inftantly defcends upon the explosion, and as fuddenly afcends again. After a few vibrations, none of which except the firft are of any great extent, it feemingly fixes at a point lower than where it stood before the explofion. But even when the gage has acquired this point of apparent reft, it still continues rifing for a confiderable time, although by fuch imperceptible degrees, that it can only be discovered by comparing its place at diftant intervals: however, it will not always continue to afcend; but will rife flower and flower, till at last it will be abfolutely fixed at a point lower than where the mercury flood before the explofion. The fame circumftances nearly happen, when powder is fired in the upper part of an unexhausted tube, whofe lower part

is immerfed in water.

"That the elafticity or pressure of the fluid produced by the firing of gunpowder is, cateris paribus, directly as its denfity, may be proved from hence, that if in the fame receiver a double quantity of powder be let fall, the mercury will fubfide twice as much as in the firing of a fingle quantity. Alfo the defcents of the mercury, when equal quantities of powder are fired in different receivers, are reciprocally as the capacities of thofe receivers, and confequently as the denfity of

produced fluid in each. But as, in the ufual method of Than trying this experiment, the quantities of powder are fo very small that it is difficult to ascertain these proportions with the requifite 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 fixteenth part of an ounce avoirdupois of powder, the receiver being firft nearly exhaufted; the mercury, after the explosion, was fubfided two inches exactly, and all the powder had taken fire. Then heating the iron a fecond time, and exhaufting the receiver as before, two drachms were let down at once, which funk the mercury three inches and three quarters; and a small part of the powder had fallen befide the iron, which (the bottom of the receiver being wet) did not fire, and the quantity which thus escaped did appear to be nearly fufficient, had it fallen on the iron, to have funk the mercury a quarter of an inch more; in which case the two defcents, viz. two inches and four inches, would have been accurately in the proportion of the respec tive 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 deter mination of this kind can take place, it is neceffary to afcertain the particular fpecies of powder that is propofed to be used. (Here Mr Robins determines in all his experiments to make ufe of government-powder, as confifting of a certain and invariable proportion of materials, and therefore preferable to fuch kinds as are made according to the fancy of private perfons.)

"This being fettled, we muft further premise these two principles: 1. That the elafticity of this fluid increafes by heat and diminishes by cold, in the fame manner as that of the air; 2. That the denfity of this fluid, and confequently its weight, is the fame with the weight of an equal bulk of air, having the fame clafticity and the fame temperature. Now from the laft experiment it appears, that of an ounce a voirdupois or about 27 grains Troy of powder, funk the gage, on its explofion, two inches; and the mercury in the barometer ftanding at near 30 inches, ths of an ounce avoirdupois, or 410 grains Troy, would have filled the receiver with a fluid whose clatticity would have been equal to the whole preffure of the atmosphere, or the fame with the elafticity of the air we breathe; and the content of the receiver being about 520 cubic inches, it follows, that ths of an ounce of powder will produce 520 cubic inches of a fluid poffeffing the fame degree of elafticity with the common air; whence an ounce of powder will produce near 575 cubic inches of fuch a fluid.

"But in order to ascertain the density of this fluid, we must confider what part of its elatticity, 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 manifeftly lefs than that of boiling water, which is known to increafe the elafticity of the air to fomewhat more than of its augmented quantity; I collect from hence and other circumftances, that the augmentation of clafticity from this cause was about of the whole: that is, if the fluid arifing from the explofion had been reduced to the temperature of the external air, the defcent of