RES
direction of the body ; circulate, in Corns meafure, towards the hinder part of the body, thereby to reftore the equili- brium, which the confhnt influx of the fiutd behind the body would otherwife deftroy ; whence the progreffive mo- tion of the fluid, and confequently the rejjiance of the body, which depends thereon, would be, in this inftance, much lefs than in our firft hypothefis, where each particle was fuppofed to acquire, from the ftroke of the reftfting body, a velocity equal to that, with which the body moved, and in the fame direction. Sir ifaac Newton has determined, that the refijlancc to a cylinder, moving in the direction of its axis, in fuch a comprefled fluid as we have here treated of, is but one fourth part of the rejjiance, which the fame cy- linder would undergo, if it moved with the fame velocity, in a fluid, constituted in the manner we have defcribed in our firft hypothefis, each fluid being fuppofed to be of the fame denfity.
But again, it is not only in the quantity of their rejijiance that thefe fluids differ, but likewife in the different manner, in which they act on folids of different forms moving in them. Wehavefhewn, that in thedifcontinued fluid, which we firft defcribed, the obliquity of the foremoft furface of the moving body would diminiih the rejijiance ; but in comprefl'ed fluids this holds not true, at leaft not in any confiderable degree j for the principal rejijiance in comprefled fluids arifes from the greater or lefler facility, with which the fluid, impelled by the forepart of the body, can circulate towards its hinder- moft part; and this being little, if at all, affected by the form of the moving body, whether it be cylindrical, co- nical, or fpherical, it follows, that while the tranfverfe fec- tion of the body, and confequently the quantity of impelled fluid is the fame, the change of figure in the body will fcarcely affect the quantity of its rejijiance. And this cafe, that is, the rejijiance of a compreffed fluid to a folid, moving in it with, a velocity much lefs than what the parts of the fluid would acquire from their compreffion ; this cafe, I fay, has been very fuliy confidercd by Sir Ifaac Newton, who has afcertained the quantity of fuch a rejift- ance, according to the different magnitudes of the moving body, and the denfity of the fluid. But he very exprefsly informs us, that the rules he has laid down are not gene- rally true, but upon a fuppofition that the compreffion of the fluid be increafed in the greater velocities of the moving body : however, fome unfkilful writers who have followed him, overlooking this caution, have applied his determina- tions to bodies moving with all kinds of velocities, with- out attending to the different compreflions of the fluids they were rejjied by ; and by this means they have accounted the rejjiance of the air to muilcet and cannon-mot, to be but one third part of what it is found to be by experience. Indeed, from all we have faid, it appears plain enough, that the rejijiing power of the medium muft be increafed, when the rejijiing body moves fo faft, that the fluid. cannot inftantaneoufly prefs in behind it, and fill the deferted fpace ; for when this happens, the body will he deprived of the prefliire of the fluid behind it; which in fome meafure ba- lanced its rejijiance, and muft fupport on its forepart the ■whole weight of a column of the fluid, independent of the motion it gives to the parts of the fluid ; and befides, the motion In the particles driven before the body, is, in this cafe, lefs affected by the compreffion of the fluid, and con- fequently they are lefs deflected from the direction, in which they are impelled by the refiftedfurfz.es ; whence this fpecies of rejijiance approaches more and more to that defcribed in our firft hypothefis, where each particle of the fluid being unconnected with the neighbouring ones, it purfued its own motion, in its own direction, without being interrupted or deflected by their contiguity ; and therefore, as we before obferved, that the rejijiance of a difcontinued fluid to a cy- linder, moving in the direction of its axis, was four times greater than the rcfijiance of a fluid fufficiently compreffed of the fame denfity, it follows, that the rejijiance of a fluid, when a vacuity is left behind the moving body, may be near four times greater than that of the fame fluid, when no fuch vacuity is formed ; for when a void fpace is thus left, we have fhewn the rejjiance to approach, in its nature, to th; of a difcontinued fluid.
This then may probably be the cafe in a cylinder moving in the fame compreffed fluid, according to the different de- grees of its velocity ; fo that if it fet out with a great velo- Ci }Y, and moves in the fluid till that velocity be much dimi- mfhed, the refitting power of the medium may be near four times greater in the beginning of its motion than in the end. Jn a globe the difference will not be fo great, becaufe, on account of its oblique furface, its rejjiance in a difcon- tinued medium, is but about twice as much as in one pro- perly compreffed ; for its oblique furface diminifhes its re- jijiance in one cafe, and not in the other : however, as the compreffion of the medium, eren when a vacuity is left be-
- he moving body, may yet confine the oblique motion
of the parts of the fl
uid, which are driven before the bodv. g„;a /^ : ■ i .l -M , r - 1
and
dC f UPp! C V denfki ° n in thoIb partS > '* is hi S hl y P^bable,
as in an elaftic fluid (as is our air) there will be fom
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that the rejjiance of a globe, moving in a compreffed fluid with a very great velocity, will be between that of a globe and of a cylinder, in a difcontinued medium; that is, , (in proportion to its velocity) we mayfuppofc it be more than twice, and lefs than four times the rejjiance of the fame globe, moving flowly through the fame medium; whence, perhaps, we (hall not much err in fuppofing the globe in its fwifteft motions to be refilled near three times more, in. pro- portion to its velocity, than when it is floweft. And as this increafe of the rejijiing power of the medium will take place, when the velocity of the moving body is fo great, that a perfect vacuity is left behind it, fo fome degree of augmentation will be fenfible in velocities much fliort of this ; for even when, by the compreffion of the fluid, the fpace left behind the body is inftantaneoufly filled up ; yet, if the velocity, with which the parts of the fluid rufii in be- hind, is not much greater than that, with which the body moves ; the fame reafons we have urged above, in the cafe of an abfolute vacuity, will hold in a lefs degree in this in- fiance ; and therefore we are not to fuppofe, that, in the increafed rejjiance, which we have hitherto treated of, it im^ mediately vanifhes, when the compreffion of the fluid is juit fuflicient to prevent a vacuum behind the rejijied body ; but we muft confider it as diminiihing only, according as the velocity, with which the parts of the fluid follow the body, exceeds that with which thebody.moves. Hence then we conclude, that if a globe fets out in a refft- /ȣ_ medium, with a velocity much exceeding that with which the particles of the medium would rum into a void fpace, in confequence of their compreffion, fo that a vacu- um is ncceflarily left behind the globe in its motion ; the rejijiance of this medium to the globe will be near three times greater, in proportion to its velocity, than what we are fure, from Sir Ifaac Newton, would take place in a flower motion. We may further conclude,, that the rejiji- ing power of the medium will gradually diminifli, as the velocity of the globe decreafes, till at laft, when it moves with velocities which bear but a fmall proportion to that, with which the particles of the medium follow it, the re- jjiance becomes the fame with what is affigned by Sir Ifaac Newton in the cafe of a comprefled fluid. And from this determination we may learn how falfe that pofition is, which afferts the refiftance of any medium to be in the duplicate proportion of the velocity of the rejijied body ; for it plainly appears, by what we have faid,' that this can only be confidered as nearly true in fmall variati- ons of velocity, and can never be applied in the comparing together the refjiances to all velocities whatever, without the moft enormous errors. See new Principles of Gun- nery, by Mr. Robins, Part 2. Prop. i.
As to the rejijiance of the air, it has been thus determined from experiments. Mr. Robins, in his New Principle of Gunnery, pag. 74, 75, &c. having taken a mufket barrel, and charging it fucceffively with a leaden ball of three quar- ters of an inch diameter, and about half its weight of powder, and taking fuch precaution in weighing of the powder, and placing it, as to be fure, by many previous trials, that the velocity of the ball could not differ by 20 feet in 1 ' from its medium quantity. It was fired againfta pendu- lum (defcribed under the headGuNNERy, append.) placed at 25 feet, 75 feet, and at 125 feet diftance from the mouth of the piece respectively. In the firft cafe it impunged againft the pendulum with a velocity of 1670 feet in 1' ; in the fecond cafe with a velocity of 1550 feet in 1" ; and in the third cafe with a velocity of 1425 feet in %' ; fo that in paiTmg through 50 feet of air, the bullet loft a velocity of about 120, or 125 feet in 1"; and the time of its pafimg through that fpace being about T ' Ys or T ' D - of 1", the medium quantity of rejjiance muft, in thefe inftances, have been about 120 times the weight of the ball ; which, as the ball was nearly ~ of a pound, amounts to about 10 lb. avoir- dupoife.
Now if a computation be made, according to the me. hod laid down for compreffed fluids in the 38th Propof. of lib. 2- of Sir Ifaac Newton's Principia, fuppofing the weight of water to be to the weight of air, as 850 to 1, it will be found that the rejjiance- of a globe of three quarters of an inch diameter, moving with a velocity of about 1600 feet in 1", will not, on thofe principles, amount to any more than a force of 45 lb. avoirdupoife; whence wc may conclude (as the rules in that propofuion for flow motions are very accurate) that the rejijiing power of ihe air in flow motions is lefs than in fwift motions, in ihe ratio of 4;- to 10, a proportion between that of 1 to 2, and 1 to 3. Again, charging the fame piece with equal quantities of powder, and balls of the fame weight, and firing three times at the pendulum, placed at 25 feet diftance from the mouth of the piece, the medium of the velocities with which the ball impinged was 1690 feet in 1". Then re- moving the piece 175 feet from the pendulum, the velocity of the ball, at a medium of five mots, was 1300 feet in 1'. Whence the ball, in pafiing through 150 feet of air, loft a velocity of about 390 feet in 1 ' ; and the rejijiance^ com- F f f ■ puttd
