RESISTANCE. 



parts of the fluid, againft which the foremoft part of the 

 body preffes in its motion, will, inftead of being impelled 

 forwards in the direftion of the body, circulate in fome 

 rneafure towards the hinder part of it, thereby to reftore 

 the equilibrium, which the conltant influx of the fluid 

 behind the body would otherwife deftroy ; whence the 

 progreffive motion of the fluid, and confequently the re- 

 fiftance of the body, which depends on it, would be in 

 this inftance much lefs than in the hypothefis, where each 

 particle is fuppofed to acquire, from the ftroke of the re- 

 filling body, a velocity equal to that with which the body 

 moved, and in the fame direftion. Sir Ifaac Newton has 

 determined, that the refdtance of a cylinder, moving in 

 the direftion of its axis, in fuch a compreffed fluid as we 

 have here treated of, is but one-fourth part of the refiftance 

 which the fame cylinder would undergo, if it moved with 

 the fame velocity,' in a fluid conftituted in the manner de- 

 fcribed in the firit hypothefis, each fluid being fuppofed to 

 be of the fame denfity. 



But again, it is not only in the quantity of their refift- 

 ance that thefc fluids differ, but likewife in the different 

 manner in which they aft on fob'ds of different forms, mov- 

 ing in them. In the difcontinued fluid, tirft defcribed, the 

 obliquity of the foremoft furface of the moving body 

 would diminifh the refiftance ; but in comprefled fluids this 

 holds not true, at leaft not i:i any confiderable degree ; for 

 the principal refiftance in compreffed fluids arifes from the 

 greater or leffer facility with which the fluid, impelled by 

 the fore-part of the body, can circulate towards its hinder- 

 moft part ; and this being little, if at all, affefted by the 

 form of the moving body, whether it he cylindrical, conical, 

 or fpherical, it follows, that while the tranfverfe feft ion of 

 the body, and confequently the quantity of impelled fluid 

 is the fame, the change of figure in the body will fcarcely 

 affeft the quantity of its refiftance. 



And this cafe, that is, the refiftance of a compreffed fluid 

 to a folid, moving in it with a velocity much lels than what 

 the parts of the fluid would acquire from their compreflion ; 

 this cafe has been very fully conlidered by fir Ifaac Newton, 

 who has afcertained the quantity of fuch a refiftance ac- 

 cording to the different magnitudes of the moving body, 

 and the denfity of the fluid. But he very exprefsly in- 

 forms us, that the rules he has laid down are not generally 

 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- 

 tion to bodies moving with all kinds of velocities, without 

 attending to the different comprefiior.s of the fluids they 

 are refitted by ; and by this means they have accounted 

 the refiftance of the air .to miifket and cannon-fhot, to 

 be but one -third part of what it is found to be by ex- 

 perience. 



It is indeed evident, that the refilling power of the 

 medium mult be increafed, when the refilling body moves 

 fo fait that the fluid cannot inftantaneoufly preis in behind 

 it, and fill the deferted fpace ; for when this happens the 

 body will be deprived of the preilure of the fluid behind 

 it ; which in fome rneafure balanced its refiftance, and muft 

 fupport on its fore-part 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 affefted by the com- 

 preffion of the fluid, and confequently they are lefs deflefted 

 from the direftion in which they are impelled by the refilled 

 furface ; whence this fpecies of refiftance approaches more 

 and more to that defcribed in the firft hypothefis, where 



each particle of the fluid being unconnected with the neigh- 

 bouring ones, it purfues its own motion, in its own direc- 

 tion, without being interrupted or deflefted by then 

 contiguity ; and therefore, as the refiftance of a difcon- 

 tinued fluid to a cylinder, moving in the direftion of its 

 axis, is four times greater than the refiftance of a fluid 

 fufficiently compreffed ct the fame denfity; it follows, that 

 the refiftance of a fluid, when a vacuity is left behind the 

 moving body, may be nearly four times greater than that of 

 the fame fluid, when no fuch vacuity is formed ; for when a 

 void fpace is thus left, the refiftance approaches in its na- 

 ture to that of a difcontinued fluid. 



This, then, may probably be the cafe in a cylinder moving 

 i;; the fame compreffed fluid, according to the different de- 

 grees of its velocity ; fo that if it fet out with a great velo- 

 city, and moves in the fluid till that velocity be much 

 diminifhed, the refilling power of the medium may be 

 nearly four times greater in the beginning of its motion 

 than in the end. 



In a globe the difference will not be fo great, becaufe, 

 on account of its oblique furface, its refiftance in a dif- 

 continued medium is but about twice as much as in one 

 properly comprefled ; for its oblique furface diminifhes its 

 refiftance in one cafe, and not in the other : however, as 

 the compreffion of the medium, even when a vacuity is left 

 behind the moving body, may yet confine the oblique mo- 

 tion of the parts of the fluid, which are driven before the 

 body, and as in an elaftic fluid, as the air is, there will be 

 fome degree of condenfation in thofe parts ; it is highly 

 probable, that the refiftance of a globe moving in a com- 

 prefled fluid may greatly exceed the proportion of die re- 

 finance to flow motions. 



And as this increafe of the refitting power of the medium 

 will take place, when the velocity of the moving body is fo 

 great that a pcrfeft vacuum is left behind it, fo fome degree 

 of augmentation will be fenfible in velocities much fhort of 

 this ; for even when, by the compreflion of the fluid, the 

 fpace left behind the body is inftantaneoufly filled up ; yet, 

 if the velocity with which the parts of the fluid rufli in be- 

 hind, is not much greater than that with which the body 

 moves, tiie fame reafons we have urged above, in the cafe 

 of an abfolute vacuity, will hold in a lefs degree in this in- 

 ftance ; and therefore we are not to fuppofe, that, in the 

 increafed refiftance which we have hitherto treated of, it 

 immediately vanifhes, when the compreffion of the fluid is 

 jull fufficient to prevent a vacuum behind the refitted body ; 

 but we mult confidcr it as diminifhing only, according as the 

 velocity with which the parts of the fluid follow the body, 

 exceeds that with which the body moves. 



Hence, then, we may conclude, that if a globe fets out in 

 a refilling medium, with a velocity much exceeding that with 

 which the particles of the medium would rufh into a void 

 ipace, in confequence of their compreflion, fo that a vacuum 

 is necellarily left behind the globe in its motion : the refin- 

 ance of this medium to the globe will be near three times 

 greater, in proportion to its velocity, than what we are fure, 

 from fir Ifaac Newton, would take place in a flower motion. 

 We may alio farther conclude, that the refilling power of 

 the medium will gradually dimii'ifh as the velocity of the 

 globe decreafes, till at lalt, when it moves with a velocity 

 which bears but a fmall proportion to that with which the . 

 particles of the medium follow it, the refiftance becomes the 

 fame with what is affigned by fir Ifaac Newton in the cafe of 

 a comprefled fluid. 



And from this determination we fee how falfe that po- 

 fition is, which aileits the refiftance of any medium to be 

 in the duplicate proportion of the velocity of the refitted 



body ; 



