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projection given. From these two data find out the impetus at that point; then 2 x 16 feet 1 inch is the velocity acquired by the descent of a body in a second of time ; the square of which (4 x the square of 16 feet 1 inch) is to the square of the velocity required, as 16 feet 1 inch is to the impetus at the point given; wherefore multiplying that impetus by four times the square of 16 feet 1 inch, and dividing the product by 16 feet 1 inch, the quotient will be the square of the required velocity; whence this rule. Multiply the impetus by four times 16 feet 1 inch, or 64 feet-J, and the square root of the product is the velocity.
Thus suppose the impetus at the point of projection to be 3,000. and the perpendicular height of the other point 100; the impetus at that point will be 3,900. Then 2,900 feet multiplied by 64,- feet gives 186,566 feet, the square of 432 nearly, the space which a body would run through in one second, if it moved uniformly.
And to determine the impetus or height, from which a body must descend, so as at the end of the descent it may acquire a given velocity, this is the rule :
Divide the square of the given velocity (expressed in feet run through in a second) by 64$ feet, and the quotient will be the impetus.
The duration of a projection made perpendicularly upwards, is to that of a projection in any other direction whose impetus is the same, as the sine complement of the inclination of the plane of projection (which in horizontal projections is radius) is to the sine of the angle contained between the lime of direction and that plane.
Draw out A f (fig. 8,) till it meets mB continued in E, the body will reach the mark B in the same time it would have moved uniformly through the line A E; but the time of its fall through M A the impetus, is to the time of its uniform motion through A E, as twice the impetus is to A E. And therefore the duration of the perpendicular projection being double the time of its fall, will be to the time of its uniform motion through A E ; as four times the impetus is to A E; or as A E is to E B; that is, as A t is to ID; which is as the sine of the angle t D A (or M A B its complement to a semicircle) is the sine of the angle t A D.
Hence the time a projection will take to arrive at any point in the curve, may be
found from the following data, 'e. the impetus, the angle of direction, and the inclination of the plane of projection, which in this case is the angle the horizon1 makes with a line drawn from the point of projection to that point.
Hence also in horizontal cases, the durations of projections in different directions with the same impetus, are as the sines of the angles of elevation. But in ascents or descents their durations are as the sines of the angles which the lines of direction make with the inclined plane. Thus, suppose the impetus of any projection were 4,500 feet; then 16 feet 1 inch: l": • 4,500 feet: 375" the square of the time a body will take to fall perpendicularly through 4,500 feet, the square root of which is 16 ' nearly, and that doubled gives 32" the duration of the projection made perpendicularly upwards. Then to find the duration of a horizontal projection at any elevation, as 20°; say K :S. angle 20° : : 32" : duration of a projection at that elevation with the impetus 4,500. Or if with the same impetus a body at the direction of 35° was projected on a plane inclined to the horizon 17°, say as sine 73°: sine tip : : 32" : duration required.
The tables in the next leaf, at one view, give all the necessary cases as well for shooting at objects on the plane of the horizon, with proportions for their solutions, as for shooting on ascents and descents. We shall in this place mention some of the more important maxims laid down by Mr. Robins, as of use in practice, l. In any piece of artillery, the greater quantity of powder with which it is charged, 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. The ranges of pieces at a given elevation, are no 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 the same as possible, will yet range to very different distances. 5. The greatest part of the uncertainty in the ranges of pieces, arises from the resistance of the air. 6. The resistance of the air acts upon projectiles by opposing their motion, and diminishing celerity; and it also diverts them from the regular track which they would otherwise follow. 7. If the same piece of cannon be successively fired at an invariable
TABLE II. For Projections on Ascents and Descents. Fig. 8, 9.
GUNPOWDER, a composition of nitre, sulphur, and charcoal, mixed together, and usually granulated. This easily takes fire, and when fired it rarefies or expands with great vehemence, by means of its elastic force. It is to this powder that we owe all the effect and action of guns, and ordnance of all sorts, so that fortification, with the modern military art, &c, in a great measure depends upon it.
The invention of gunpowder is ascribed by Polydore Virgil to a chemist, who having accidentally put some of his composition in a mortar, and covered it with a stone, it happened to take fire, and blew up the stone. Thevet says, that the person here spoken of was a monk of Fribonrg, named Constantine Anelzen; but Belleforet, and other authors, with more probability, hold it to be Bartholdus Schwartz, or the black, who discovered it, as some say, about the year 1320; and the first use of it is ascribed to the Venetians in the year 1380, during the war with the
Genoese. But there are earlier accounts of its use, after the accident of Schwartz, as well as before it: for Peter Mexia, in his "Various Readings," mentions that the Moors being besieged, in 1343, by Alpbonstis the Eleventh, King of Castile, discharge;! a kind of iron mortars upon them, which made a noise like thunder: and this is seconded by what is related by Don Pedro, Bishop of Leon, in his Chronicle of King Alphonsus, who reduced Toledo, riz. that in a sea combat between the King of Tunis, and the moorish King of Seville, about that time, those of Tunis had certain iron tubs or barrels, with which they threw thunderbolts of fire.
Du Cange adds, that there is mention made of gunpowder in the registers of the chambers of accounts in France, as early as the year 1338. But it appears that Roger Bacon knew of gunpowder near one hundred years before Schwartz was born; and M. Dntens carries the antiquity of gunpowder still'much higher, and refers to the writings of the ancients themselves for the proof of it It appears too, from many authors and many circumstances, that this composition has been known to the Chinese and Indians for thousands of years.
For some time after the invention of artillery, gunpowder was of a much weaker composition than that now in type, or that described by Marcus Graecus, which was chiefly owing to the weakness of their first pieces. Of twenty-three different compositions, used at different times, and meuI tioned by Tartaglia in his " Ques. and Inv. lib. 3, ques. 5;" the first, which was the oldest, contained equal parts of the three ingredients. But when guns of modern structure were introduced, gunpowder of the same composition as the present came into use. In the time of Tartaglia the cannon powder was made of four parts of nitre, one of sulphur, and one of charcoal; and the musket-powder of forty-eight parts of nitre, seven parts of sulphur, and eight parts of charcoal; or of eighteen parts of nitre, two parts of sulphur, and three parts of charcoal. But the modern composition is six parts of nitre, to one of each of the other two ingredients: though Mr. Napier says, he finds the strength commonly to be greatest when the proportions are, nitre three pounds, charcoal about nine ounces, and sulphur about three ounces. See his paper on gunpowder in the Transactions of the Royal Irish Academy, vol. 11. The cannon-powder was in meal, and the musket-powder grained; and it is certain, that the graining of powder, which is a very considerable advantage, is a modern imprqvement.
To make gunpowder duly, regard is to be had to the purity or goodness of the ingredients, as well as the proportions of them, for the strength of the powder depends much on that circumstance, and also on the due working or mixing of them together. See Niter.
These three ingredients in their purest state being procured, long experience has shown that they are then to be mixed together in the proportion before-mentioned, to have the best effect, riz. three quarters of the composition to be nitre, and the other quarter made up of equal parts of the other two ingredients, or, which is the same thing, six parts nitre, one part sulphur, and one part charcoal.
But it is not the due proportion of the materials only, which is necessary to the making of good powder, another circum
stance, not less essential, is the mixing them well together; if this be not effectually done, some parts of the composition will have too much nitre in them, and others too little; and in either case there will be a defect of strength in the powder.
After the materials have been reduced to fine dust, they are mixed together, and moistened with water, or vinegar, or urine, or spirit of wine, &c, and then beaten together for twenty-four hours, either by hand or by mills, and afterwards pressed into a hard, firm, solid cake. When dry, it is grained or corned, which is done by breaking the cake of powder into small pieces, and so running it through a sieve; by which means the grains may have any size given them, according to the nature of the sieve employed, either finer or coarser; and thus also the dust is separated from the grains, and again mixed with other manufacturing powder, or worked "P into cakes again.
Powder is smoothed or glazed, as it is called, for small arms, by the following operation: a hollow cylinder or cask is mounted on an axis, turned by a wheel; this cask is half filled with powder, and turned for six hours, and thus by the mutual friction of the grains of powder it is smoothed or glazed. The fine mealy part, thus separated or worn off from the rest, is again granulated.
The velocity of expansion of the flame of gunpowder, when fired in a piece of artil. lery, without either bullet or other body before it, is prodigiously great, viz. seven thousand feet per second, or upwards, as appears from the experiments of Mr. Robins. But M. Bernoulli and M. Euler suspect it is still much greater; and Dr. Hutton supposes it may not be less, at the moment of explosion, than four times as much.
It is this prodigious celerity of expansion of the flame of gunpowder which is its peculiar excellence, and the circumstance in which it so eminently surpasses all other inventions, either ancient or modern; for as to the momentum of these projectiles only, many of the warlike machines of the ancients produced this in a degree far surpassing that of our heaviest cannon shot or shells; but the great celerity given to these bodies, cannot be in the least approached by any other means but the flame of powder.
T» prove gunpowder. There are several ways of doing this. l. By sight; thus, if it be too black, it is a sign that it is moist, or else that it has too much charcoal in it; so also if rubbed upon white paper it blackens it more than good powder does j but if it be of a kind of azure colour, somewhat inclining to red, it is a sign of good powder, t. By touching; for if in crushing it with the fingers' ends, the grains break easily and turn into dust, without feeling hard, it has too much coal in it; or if, in pressing it under the fingers upon a smooth hard board, some grains feel harder than the rest, it is a sign the sulphur is not well mixed with the nitre. Also by thrusting the hand into the parcel of powder, and grasping it, as if to take out a handful, you will feel if it is dry and equal grained, by its evading the grasp and running mostly out of the hand. 3. By burning; and here the method most commonly followed for this purpose with us, says Mr. Robins, is to fire a small heap of it on a clean board, and to attend nicely to the flame and smoke it produces, and to the marks it leaves behind on the board; but besides this uncertain method, there are other contrivances made use of, such as powder-triers, acting by a spring, commonly sold at the shops, and others again that move a great weight, throwing it upwards, which is a very bad sort of eprouvette.
The best eprouvette consists in a small cannon, the bore of which is about one inch in diameter, and is usually charged with two ounces of powder, and with powder only, as a ball is not necessary, and the strength of the powder is accurately shown by the arc of the gun's recoil. The whole machine is so simple, easy, and expeditious that, as Dr. Hutton observes, the weighing of the powder is the chief part of the trouble, and so accurate and uniform, that the successive repetition, or firings, with the same quantity of the same sort of powder, hardly even yield a difference in the recoil of the one hundredth part of itself.
To recover damaged powder. The method of the powder merchants is this: they put part of the powder on a sail-cloth, to which they add an equal weight of what is really good, then with a shovel they mingle it well together, dry it in the sun, and barrel it up, keeping it in a dry and proper place.
Others again, if it be very bad, restore it by moistening it with vinegar, water, urine, •r brandy, then they beat it fine, sift it, and to every pound of powder add an ounce, or an ounce and a half, or two ounces (according as it is decayed) of melted nitre, and afterwards these ingre
dients are to be moistened and well mixed, so that nothing may be discerned in the composition, which may be known by catting the mass, and then they granulate it as useful. In case the powder be quite spoiled, the only way is to extract the saltpetre with water, in the usual way, by boiling, filtrating, evaporating, and crystallizing, and then with fresh sulphur and charcoal to make it up afresh.
On the subject of gunpowder, see also Euler on Robins's Gunnery, Antoni Examen de la Poudre, Baume's Chemistry, and Thompson's Experiments in the Philos. Trans, for 1781.
Soon after the discovery of the oxygenated-muriatic acid, and its combination with potash, it was found that this oxymuriate produced a much more violent detonation with combustible bodies, than is afforded by nitre. It has been estimated to possess more than double the force ; but on account of this extraordinary power in' gunpowder made with the new salt, and some fatal accidents by its exploding in consequence of friction or percussion to which it is liable, as well during the manufacture as afterwards, this modern compound has not been brought into use in military operations, but is likely to continue among the articles of scientific curiosity.
Gunpowder and Combustibles. No person shall make gunpowder but in the regular manufactories established at the time of making the statute 12 George III. c. 61 or licensed by the sessions, pursuant to certain provisions, under forfeiture of the gunpowder, and two shillings per pound; nor are pestle mills to be used under a similar penalty.
Only forty pounds of powder is to be made at one time under one pair of stones, except Battle-powder, made at Battle and elsewhere in Sussex.
Not more than forty hundred weight to be dried at one time in one stove; and the quantity only required for immediate use to be kept in or near the place of making, except in brick or stone magazines, fifty yards at least from the mill. «.
Not more than twenty-five barrels to be carried in any land carriage, nor more than two hundred barrels by water, unless going by sea or coastwise, each barrel not to contain more than one hundred pounds.
No dealer to keep more than two hundred pounds of powder, nor any person not a dealer, more than fifty pound in the