Page:Cyclopaedia, Chambers - Supplement, Volume 2.djvu/864

 GUN

G U N

See New Princip. of Gunnery, p. 28, 29, &c. See alfo the Phil. Tranf. N. 469, p. 444.. where a final] correction, relat- ing to a number in Mr. Robins's 8th proportion, is men- tioned.

It is to be obferved, that the length to which the ribbon b drawn, is always nearly the chord of the arch defcribed by theafcent; it being fo placed, as to differ infenfibly from thofe chords which mod frequently occur ; and thefe chords are known to be in the proportion of the velocities of the pendulum acquired from the ftroke. Hence it follows, that the proportion between the lengths of ribbon drawn out at different times, will be the fame with that of the velocities of the impinging bullets.

Now from the computations delivered' by Mr. Robins, it appears, that the velocity of the bullet was 1641 feet in one fecond of time, when the chord of the arch defcribed by the afcent of the pendulum, in confequence of the blow, was 1 7x inches. Therefore, by the proportion of any other lengths of ribbon drawn out, by any percuffion, to 174-, the proportion of the velocity with which the bullets im- pinge, to the known velocity of 1641 feet in 1", will be de- termined.

As experiments of this kind are often attended with danger and difficulty, thofe who may be difpofed to make any, will find feveral ufeful practical cautions, in p. 31, 32 and 33 of the faid Treatife.

By the experiments recited at large, in Propofition IX. of the fameTreatife, it appears, that the computations from Mr. Ro- bins's theory, compared with thofe experiments, which were made with barrels of various lengths, from feven inches to forty-five, and with different quantities of powder, from fix penny-weight to thirty-fix, have a remarkable coinci- dence, and fuch as occurs but in few philofophical fubjech of fo complicated a nature.

Suppofing, for inftance, the length of a barrel to be 45 inches, the quantity of powder 12 penny-weight, and the ball I inch diameter, weighing 14- ounce, or tV of a pound averdupoife, and the windage or excefs of the diameter of the barrel above that of the bullet about _* &. of an inch ; the velocity of the bullet wiil, by theory, be about 1670 feet in one fecond : and this velocity is found in thefe experiments, to be the mean velocity which the ball really receives in thofe circumftances. Hence we may determine the velocities with which mufket and cannon fhot are dilcharged from their refpe£tive pieces by their ufual allotment of powder. For as a leaden ball of I inch diameter, and weighing near- ly 1 j ounce averdupoife, being fired from a barrel of 45 in- ches in length with half its weight of powder, will have a velocity at its iffuing from the piece, which, if uniformly continued, would carry it near 1700 feet in 1": fo if in- stead of a leaden ball an iron one of the fame diameter was placed in the fame fituation in the fame piece, and was im- pelled by the fame quantity of powder, the velocity of fuch an iron bullet would be greater than that of the leaden one, in the fubduplicate ratio of the fpecific gravities of lead and iron; and fuppofing that ratio to be as 3 to 2, and comput- ing on the foregoing principles, it will appear, that an iron bullet of 24 lb. weight, fhot from a piece of 10 feet in length, with 16 lb. of powder, will acquire from the cxplo- fion a velocity which, if uniformly continued, would carry it nearly 1650 feet in 1". But if inftead of this full charge weighing two thirds of the ball, we fuppofe the charge to be only half that weight, then its velocity will be no more than at the rate of 1490 feet in 1" ; and the fame would be the velocities of every leffer bullet, fired with the fame pro- portions of powder, if the lengths of all pieces were con- ftantly in the fame ratio with the diameters of their bore : and tho' this proportion does not always hold, yet the dif- ference is not confiderable enough to occafion a very great variation from the velocities here affigned. But in thefe de- terminations, the windage is fuppofed to be no more than is juft neceffary for the eafy putting down the bullet ; whereas in real fervice, either thro' negligence or unfkilfulnefs, it of- ten happens, that the diameter of the bore fo much exceeds the diameter of the bullet, that great part of the inflamed fluid efcapes by its fide ; whence the velocity of the fhot may, in this cafe, be confiderably lefs than what is here af- figned : however, part of this may poiiibly be compenfated by the greater heat which in all probability attends the firi'iv* of thele large quantities of powder.

The theory here eftahlifhed fuppofes what is faid under the head Gun-powder, that the powder when fired is equally hot with iron at the beginning of its white heat ; but in very fmall quantities of powder the heat is probably lefs, and confequently the elafticity lefs than what arifes from this fup- pcfition. Now this decreafe of elafticity in fmall quantities of powder has been found in many trials actually to take place. For inftance, according to the theory before laid down, the velocity given the ball by the action of the powder is in round numbers 1670 feet in 1" ; and this, as has been faid, is confirmed by the experiments taken at a medium. If now the barrel and pofttion of the ball remaining the fame, there be placed in the fpace that contained 12 penny-weight of

powder there mentioned, only one penny-weight; it follows, that if the elafticity of the fmaller charge be the fame in proportion to its quantity with that of the larger, then the velocity of the bullet, when impelled by the explofion of the fmaller charge, will be to the velocity of a bullet impelled by a greater charge in the fubduplicate ratio of the quantities cf the refpective charges, that is, in the fubduplicate ratio of 1 to j 2. Confequently the velocity communicated by 12 penm-weight being known to be that of 1670 feet in 1", the velocity communicated by one penny-weight would be that of 482 feet in 1" nearly; but by repeated trials differ- ing little from each other, it has been found, that the real velocity acquired by the ball in this cafe, from the explofion of one penny-weight, was rather lefs than that of 400 feet in 1". Whence it is evident, that the elafticity of one penny-weight of powder, when fired, is lefs in proportion to its quantity than that of 12 penny- weight, as it ought to be by the theory.

So if three penny-weight of powder be placed in the fame manner with the one penny-weight laft mentioned, the real velocity the ball will acquire from the explofion, will be from 740 to 720 feet in 1" . Whereas, fuppofing the elafticity of three penny-weight, when fired, to be in fimilar circum- ftances the fame with that of 12 penny-weight, the velocity acquired by the ball fhould be 835 feet in 1' . It is farther to be obferved, that the theory eftablifhed under the head Gun-powder, fuppofes that in fhe firing of gun- powder about -rV of its fubftance is converted by the fudden inflammation into a permanent elaftic fluid, the elafticity of which, in proportion to its heat and denfity, is the fame with that of the common air in the like circumftances : it farther fuppofes, that all the force exerted by gun-powder in its moft violent operations, is no more than the action of the elafti- city of the fluid thus generated ; and thefe principles enable us to determine the velocities of bullets impelled from fire arms of all kinds.

From this theory appears the inconclufivenefs of what fome authors have advanced relating to the advantages of particular forms, for the chambers of mortars and cannon ; for all their laboured fpeculations on this head are evidently founded on very erroneous opinions about the actions of fired powder. See lib. cit. p. 41.

But it muft not be diffembled, that however probable this theory may be from the experiments and reafons on which it is founded, there ftill remains a difficulty which feems not yet fully accounted for. The doubt arifes from fome expe- riments made before a committee of the royal fociety, who hereupon gave it as their opinion, that the change of the form in the chamber will produce a change of the diftance to which the bullet is thrown. The experiments upon which this opinion was founded, were as follows : Three brafs chambers were made, whofe depths were re- fpetStively three inches, 1 \ inch and | inch ; fo turned as to fit the chamber of a brafs mortar exactly ; each of thefe chambers contained, when full, one ounce troy of powder. The ball was of brafs, weighing' nearly 356 ounces troy. The ball touched the powder of the charge in all thefe ex- periments. With the fir.fi: chamber of three inches deep, the elevation of the mortar being 45, the range taken at a medium of three fhot was 741 feet; and the mean diftance to which the ball was thrown with the chamber of | inch deep, was but 464 feet. As to the chamber of ii inch, it not fitting the chamber of the mortar exactly, the ranees were very irregular; but the leaft range, tho' fired late in the damp of the evening, exceeded the fartheft range of the % inch chamber, and the fartheft: range extended to 686 feet; fo that the committee feem well warranted in their opinion. The difficulty is to reconcile this with the fore- going theory. Its ingenious author has, in general obferved, in the account of his book given in the Phil. Tranf. N'?„ 469, p. 455, that when the charge is much fmaller than the ufual allotment of powder, there are fome irregularities, as thofe arifing from the different heat of fmall and large quantities of powder, to which head too perhaps muft be referred the experiments made by the committee on the effect of different fmall chambers ; but in cuftomary charges, the velocities of bullets refulting from all the experiments hitherto made, are really fuch as the theory requires. And it appears, that thefe velocities are much greater than what they have been hitherto accounted ; and there are realbns from the theory to believe, that in cannon {hot the velocities may ftill exceed the fore- going computation. See Phil. Tranf. N°. 465. If a bullet be laid at a confiderable diftance from the charge, the principles before laid down cannot then be applied to determine the velocity of the ball ; they being only appli- cable in cafes where the bullet is contiguous to the charge, or nearly fo. For by what is fhewn under the head Gun- powder, when the furface of fired powder is not confined by a heavy body, which it is obliged to impel before it, the flame dilates itfelf with a velocity much beyond what it can at any time communicate to a bullet by its continued preffure ; becaufc the powder having acquired a confiderable degree of velocity of expanfion, the firlt motion of the ball will not

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