PRO
PRO
far the refinance of the air was to be attended to, in the de- terminations of gunnery. But inftead of proceeding thus cau- tioufly, fubfequent writers have boldly afierted, that no con- fiderable variation could arife from the refiftance of the air, in the flight of fhells and cannon-fhot ; and it is now become an axiom almoft generally acquiefced in, that the flight of thefe bodies is nearly in the curve of a parabola. This hypothefis was fupported by Anderfon in his Treatife of the genuine ufe and effefls of the gun, published in 1674; alfo by Monf Blondel in his Art de jetter lei Bornbes ; and the fame fubjefl being treated of by Dr Halley in the Phil. Tranfac- tions, N°. 216. this learned gentleman, fwayed by the confideration of the great difproportion between the denfity of bullets and of the air, thinks it reafonable to believe, that the refiftance of the air to large metal fhot is fcarcely dif- cernible, although in light fhot he acknowledges it ought to be accounted for. But though this hypothefis was readily admitted by thofe who contented themfelves with fpeculation only, yet Anderfon himfelf found it impoflible to reconcile it to experience, without fome modification This led him to fuppofe that a bullet at its firft difcharge, flew a certain dif- tance in a right line, from the end of which line only it be- gan to bend into a parabola. By this means he defended, as he thought, the hypothefis of a parabolic motion : but fo ftrange a fuppofition as that of the fufpeufion of the acf ion of gravity, needs no confutation. Anderfon was deceived, by his not knowing how greatly the primitive velocity of the heavieft (hot is diminished in the courfe of its flight by the re- fiftance of the air.
Practical gunners alfo unanimoufly agree, that every mot flies in a ftreight line to a certain diftance from the piece, which imaginary diftance they call the extent of the point blank lhot. This fight in affreight line, indeed, fuppofing it facf, would be not only a refutation of the parabolic hvpothefis, but a moft unaccountable difficulty in itfclf, as implying a fufpen- fion of the action of gravity. But the great velocity of can- non-fhot, afligned by Mr. Robins, feems readily to clear up this affair. We need only fuppofe, that within the diftance thus determined by practical gunners, the deviation of the path of the fnot is not very perceptible in their way of point- ing. Now as a fhot of 24 lb. fired with two thirds of its weight in powder, will, at the diftance of five hundred yards from the piece, be feparated from the line of its original di rection, by an angle of little more than half a degree ; thofe who are acquainted with the inaccurate methods often ufed in the directing of cannon, will eafily allow, that fo fmall an aberration as this, may, by the .generality of practitioners, be unattended to, and the path of the fhot may confequently be deemed a ftrait line, efpecially as other caufes of error will often intervene, much greater than what arifes from the in- curvation of this line by gravity. See new princip. of Gun- nery, p. 82.
How rafh and erroneous the opinion of the inconfiderable refiftance of the air is, will eafily appear from what is efta- blifhed by that ingenious author, who has fllcwn that this refiftance to a cannon ball amounts to more than twenty times the weight of the ball. What errors may not be expected from an hypothefis which neglects this force as inconfiderable ? In effect, it will not be difficult to (hew, 'that the track de- fcribed by the flight of (hot or fhells, is neither a parabola nor nearly a parabola. For by that author's experiments it ap- pears, that a mufket ball of three fourths of an inch diameter, fired with half its weight of powder from a piece 45 inches long, moves with the velocity of near 1700 feet in a fecond. Now, by the common parabolic theory if this ball flew in the curve of a parabola, its horizontal range at 45 , would be found to be about 1 7 miles. But from practical writers, as Diego, Ufano, and Merfennus, it appears, that this range is fliort of half a mile ; fo that a mufket fhot at 45' eleva- tion, with a reafonable charge of powder, flies not the l r . part of the diftance it ought to do if it moved in a parabola. Nor is this great diminution of the horizontal range to be wondered at, when it is confidercd that the refiftance of thi air to this bullet, when it firft iffues from the piece, amounts to 120 times its gravity. Again, if the flight of the heavieft fhot, in common ufe for land fervicc, as of iron bullets of 241b. weight, be examined it will appear, that fuch a fhot made with a full charge of powder has a velocity of 1650 feet in 1". And the horizon tal range at 4$° of this fhot, would, according to rhe para bolic hypothefis, be about 16 miles; but by the experiments of St. Rcmy it appears, that the range is really fhort of three miles ; which is not one fifth of the diftance it ought to fly. if it defcribed the curve of a parabola
And this deviation from the parabola, happens not only ir thefe great velocities, but in fuch as are much lets ; thus in velocities of about 400 feet in 1"; by feveral experiments it appears, that the range of a leaden bullet of three fourths of an inch in diameter, fired at different elevations with this velocity, did not at all anfwer the common theory. So that it fufficiently appears that this theory, or the fuppofition of the inconiiderablenefs of the air's refiftance to projtBilei, is falfe. Indeed the falfenefs of this hypothefis almoft appears at fight, even in frojteiiks flow enough to have their motion traced by
the eye ; few there are who do not defcend thro' a curve ma- nifeftly fhorter and more inclined to the horizon than that in which they afcended, and the higheft point of their flight, or the vertex of the curve, is much nearer to the place where they fall on the ground than from whence they were at firft difcharged. Thefe things cannot be a moment doubted of by any one, who in a proper fituation views the flight of flones, arrows, or fhells, thrown to any confiderable diftance. See new princip. of Gunnery, Part 2. Prop. b. What is here advanced may be confirmed from the conftant obfervation of all who are converfant in the practice of throw- ing bombs, viz. that the ranges at elevations below 4s , con- ftantly exceed the ranges at elevations above 45 , which are reflectively at an equal diftance from 45 . Thus the range of fhells at 75°, will.'go farther than one at 6o°, and fo~a range at 20 exceeds one at 65°, EsV. but it is known that in the parabolic hypothefis thefe ought to be equal, which hy- pothefis is therefore falfe.
There is an odd phienomenon in the motion of bodies pro- je3ed with confiderable force, which fhews the great com- plication and difficulty of this fubjea. The phxnomenon is, that bullets in their flight are not only depreffed beneath their original direction by the action of gravity, but are alfo fre- quently driven to the right or left of that direaion by the ac- tion of fome other force.
If it was true that bullets varied their direaion by the aaion of gravity only, then it ought to happen that the errors in their flight to the right or left of the mark they were aimed at, fhould increafe in the proportion of the diftance of the mark from the piece only. But this is contrary to all ex- perience ; the fame piece which will carry its bullet within an inch of the intended mark, at 10 yards diftance, cannot be relied on to 10 inches in ico yards, much lefs to -o inches in 300 yards.
Now this inequality can only arife from the track of the bul- let being incurvated fideways as well as downwards ; for by this means the diftance between the incurvated line, and the line of direaion, will increafe in a much greater ratio than that of the diftance; thefe lines being co-incident at the mouth of the piece, and afterwards fcparating in the manner of a curve from its tangent, if the mouth of the piece be con- fidered as the point of contafl.
This is put beyond difpute from the experiments made by Mr. Robins ; who informs us, that having taken a barrel carrying a ball of three fourths of an inch diameter, and fix- ing it on a heavy carriage, he fatisfied himfelf of the fteadi- nefs and truth of its direaion, by firing at a board one foot and a half fquare, and miffing it but once in i6fucceffive (hot. Now the fame barrel being fixed on the fame carriage, and fired with a fmaller quantity of powder, fo that the fhock on the difcharge would be much lefs, and confequently the direflion lefs changed, he found that at 760 yards diftance the ball flew fomctimes 100 yards to the right of the line it was pointed on, and at other times 100 yards to the left. He found too that its direaion in the perpendicular line was not lefs uncertain, it falling one time above 200 yards fliort of what it did at another; altho' by the niceft examination of the piece after the difcharge, it appeared not to have the leaft flatted from the pofition it was placed in. New prin- ciples of Gunnery, Part. 2. Prop. 7.
If it be afked what can be the caufe of a motion fo different from what has been hitherto fuppofed ! It may be anfwered, That the deflcaion in queftion mill be owing to fome power a3mg obliquely to the progreffive motion of the body, which power can be no other than the refiftance of the air. And this refiftance may perhaps aa obliquely to the progreffive motion of the body, from inequalities in the refilled furface - but its general caufe is doubtlcfs a whirling motion acquired* by the bul et about its axis; for by this motion of rotation, combined with the progreffive motion, each part of the bul- let's furface will ftrike the air in a direaion very different from what it would do if there was no fuch whirl ; and the ob- liquity of the action of the air arifing from this caufe will be greater, according as the rotatory motion of the bullet is greater in proportion to its progreffive motion. PROLAPSUS aculi, in furgcry, a diftemperature of the eye, in which it is fo violently inflamed and fwelled, that it cannot be retained in its orbit or focket, but protrudes itfclf out of its natural feat. This diforder is not only attended with great deformity, but alfo intenfe pains, blindnefs, and too often an obftinate cancer are the effeas of it. This is fometimes fo violent in degree, that the eye burfts out of its coats. This diforder fometimes arifes from inflammations, or re- dundancy of humors.; and fometimes from external violence, or from a cancer. Sometimes, when the diforder is recent, and but in a moderate degree, it may be carried off by bleed- ing, bhftering, and purging, with external applications, as fomentations and the like. When it will give way to none of thefe, the tumor muft be opened, and the humors dif- charged, and this repeated as often as neceffary ; after every drefhng, binding on a plate of lead hollowed in a proper degree. r
When the natural figure of the eye, and its office of vifion are wholly deftroyed by this difeaie, and the pains become
more
