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ties are the neceflary concomitants of all complicated expe- riments : in the collifion cf bodies, in the running or fpout- ing of water, even in fmall velocities, irregularities happen, not reconcileable to theory or to each other : what may not then be fuppofed to happen from the action of fo furious a power as gun-powder? From experiments it appears, that velocities of bullets fired from the fame piece, charged with the fame powder, and all other circumftances, as nearly as poffible, the fame, do yet differ from each other by fometimes more than -J- part of the whole : but this is a fmall deerec of inaccuracy in a cafe of this nature, and if the action of the flame on the bullet, after it is out of the piece, is fo fmall as to produce no greater effect than what may be deftroyed by the inevitable variations of the experiments, the ne^lectin" it entirely is both convenient and a reafonablc procedure. Now what gives ground to think that this poftulatum, though not rigoroufly true, may be fafely affumed, is the confederation of the fpreading of the flame by its own elafticity, as (oon as it efcapes from the mouth of the piece; for by this it may be conceived that the part of it which impinges on the bullet may be neglected, although the impulfe of the flame be a very remarkable force*
With regard to the fecond aflumed principle, that all the powder is fired before the bullet is fenfibly moved from its place; it is to be obferved, that this very pofition, having been examined by a committee of the Royal Society, was, after fe- veral experiments, determined in the negative; from whence many may be ready to conclude, that the whole theory muft be overturned. But this requires a farther difcuflion, and it will appear that though this principle be not rigoroufily true, no more than the former, yet it feems alfo that it may be fafely admitted in inveftigating the effects of powder, fmce, even in fliort barrels, where the fpace the bullet was impelled thro' was not five inches, and where of courfe the deficiency of velocity was greateft, it cannot amount to one thirtieth of the whole. This will appear from the experiments made by the committee; for when the barrel was fo fhortned, that the bullet being placed clofe to the wad, lay with its outer fur- face nearly level with the mouth of the piece; yet even in this fhort tranfit of the bullet but ^ of the whole charge, at a medium, was collected unfired; which f, properly reduced amounts to but ^ of the charge. This reduction is founded on thefe confiderations, that the powder ufed by the commit- tee being unequally grained, when the fmaller grains, collect- ed by lifting, were ufed, the quantity remaining unfired was lefs at a medium in the ratio of 5 to 3, than when it was ufed without fifting. Alfo, by extracting the falt-petre from the powder collected unfired, there was lefs falt-petre contained in it than in real powder, nearly in the ratio of 9 to 7. Now thefe two proportions compounded, make the proportion of 15 to 7, in which proportion muft the quantities of powder unfired be reduced, in order to determine the quantity of fine good powder that might be fuppofed to remain unfired in the experiments brought to confirm the aforefaid theory. Now it appears by experiments, that the velocities of bullets placed in the fame fituation are in the fubduplicate proportion of the charges : confequently the deficiency of velocity arifin«- from the lofs of ^ of the charge will be about i of the ve- locity only. And in thtj experiments made with a barrel 5 i iuches in length, where the ball had not three inches to move, the quantity of real powder collected unfired from a charge of I2dwt. would have been no more than 16 grains, at a medium, or T ' g of the whole charge, which would produce a deficiency of ^ of the velocity only : a difference lefs than what frequently occurs in the exacteft repetition of the fame experiments.
This, it is thought, is fully fufficient to juftify the principle in queftion; efpecially as in all cafes of real ufe the length of the barrel, in proportion to the quantity of the charge, will be much greater than in the inftances here mentioned. See Phil. Tranf. N\ 469, p. 450, 452, &c. and fee the Experiments of the committee in the Tranfactions, N°. 465, P- *7 2 > T 73> &*
The greateft part of thofe who have written on the manner in which powder takes fire, have fuppofed it to be done by regular degrees; the firft grains firing thofe contiguous, and they the next fucceflivcly; and it has been generally thought, that a confiderable time was employed in thefe various com- munications : for Mr. Daniel Bernoulli, in his Hydro-dyna- ?nica y has concluded from fome experiments made at Peterf- burg, that the greateft part of the charge efcapes out of the piece unfired, and that the fmall part which is fired, does not take fire 'till it is near the mouth. Many theories too have been compofed on the time of the progrefs of the fire amongft the grains, and the different modifications which the force of powder did thence receive; and it has been generally conceived, that the proper lengths of pieces were determin- able from this principle; that they lliould be long enough to give time for all the powder to fire.
But no fuch regular and progreffive fteps faem obfervable in the explofion. For confidering that by loading with a greater weight of bullet, and thereby almoft doubling the time of the continuance of the powder in the barrel, its force re-
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ceiyes but an inconfiderabje augmentation; and that doubling and trebling the ufual charge, the-powder thus added always" produces a correfpondent eft'ect in the velocity of the bullet; llkewife, that in a piece near four feet in length, chawed with an ufual charge of powder, the velocity communicated to the bullet, during the firft three inches of its motion, is full half the velocity acquired in its whole pafTage thro' the bar- rel; and confidering alfo that the elafticity or force of the powder, in .the three firft inches of its expanfion, is at a medium near eight times greater than in the laft two feet of the barrel; it may be concluded from all thefe circumftances, that the time employed by the powder in taking fire was not neceflary to be attended to in thefe computations; but that the whole ma& might be fuppofed to be kindled, before the bullet was fenfibly moved from its place. And the experiments reported by the committee of the Royal Society, in the Tranfaaion, N". 465, before-mentioned, are ftrong proofs that the powder is not fired in the pro- grcfhve manner ufually fuppofed; for when the ihort barrel was charged with 12 penny- weight artd fix penny-weight re* fpeclively, the quantity of powder which was collected un- fired from 12 penny- weight, did not exceed by three grains, at a medium, what was collefied from fix penny-weight, al- though the bullet was a lefs time in patting thro' the barrel with 12 penny- weight than with fix, it having a lefs way to move; confequently the quantity remaining unfired of the fix penny-weight, did not continue unfired for want of time; fince when the piece was charged with 12 penny-weight, the additional fix penny- weight was confirmed in a'lhorter time. See Phil. Tranf. N . 469. p. 450.
Mr. Robins has alfo given us an ingenious way of determin- ing, by experiments, the velocity which any ball moves with, at any diftance-of the piece it is difcharged from. This may be effeaed by means of a pendulum made of iron, having a broad part at bottom, covered with a thick piece of wood, which is fattened to the iron by fcrews. Then having three poles joined together by their tops and fpread- ing at bottom, fuch as are vulgarly ufed in weighing and lift- ing heavy bodies, and called by workmen triangles, on two of thefe poles, towards their tops, are fcrewed on lock- ets, on which the pendulum is hung by means of a crofs piece, which becomes its axis of fufpenfion, and on which it ought to vibrate with great freedom. Something lower than the bottom of the pendulum there mould be a brace, joining the two poles to which the pendulum is fufpended; and to this brace there is fattened a contrivance made with two edges of fteel, fomething in the manner of a drawing pen; the ftrength with which thefe edges prefs on each other being diminifhed or increafed at pleafure, by means of a fcrew. To the bottom of the pendulum mould be fattened a narrow ribbon, which patting between the fteel edges, may hang loofely down by means of an opening cut in the lower piece of fteel.
The inftrument being thus fitted, if the weight of the pen dulum, the refpeciive diftances of its center of gravity, and of its center of ofcillation, from its axis of fufpenfion, be. known, it may from thence be found, what motion will be communicated to this pendulum by the percuttion of a body of a known weight moving with a known degree of velo- city, and flriking it in a given point; that is, if the pen- dulum be fuppoled at reft before the percuffion, it will be known what vibration it ought to make in confequence of fuch a blow; and if the pendulum being at reft, is ftruck by a body of a known weight, and the vibration which the pendulum makes after the blow is known, the velocity of the ftriking body may from thence be determined. Now the extent of the vibration, made by the pendulum, may be meafured by the ribbon. For if the preffure of the fteel edges on the ribbon be regulated by the fcrew, fo as to be free and eafy, tho' with fome minute refiftance to hinder its flipping of itfelf: then fetting the pendulum at reft, let the part of the ribbon between the pendulum and the fteel edges be drawn ftrait, but not drained, and fixing a pin in the part of the ribbon contiguous to the edges, the pendu- lum fwinging back by the impulfe of the ball, will draw out the ribbon to the juft extent of its vibration, which will be determined by the interval on the ribbon between the edges and the place of the pin.
The computation by which the velocity of the ball is deter- mined, from the vibration of the pendulum after the ftroke, iff founded on this principle of mechanics; That if a body in motion ftrikes on another at reft, and they are not fepa- rated after the ftroke, but move on with one common mo- tion, then that commen motion is equal to the motion with which the firft body moved before the ftroke : whence, if that common motion and the mattes of the two bodies are known,
e motion of the firft body before the ttroke is thence de-
th,
termined. On this principle it follows, that the velocity of a bullet may be diminiihed in any given ratio, by its being made to impinge on a body of a weight properly proportion- ed to it; and hereby the molt violent motions, which would otherwife efcape our examination, are eafily determined by the retarded motions which have 2 given relation to them. 4 See
