RESISTANCE. 



which a certain force is required to move the particles from 

 their places, in order to let the body pafs. 



The retardation from the firft catlfe is always the fame 

 in the fame fpace, the body remaining the fame, whatever 

 be the velocity, that is, the refinance is as the fpace run 

 , through in the fame time ; in which ratio the velocity alfo 

 increafes ; and therefore the refiftance from the firft caufe 

 is as the velocity itfelf. 



The refiltance from the fecond caufe, when the fame 

 body moves through different fluids with the fame volocity, 

 follows the proportion of the matter to be removed in the 

 fame time, which is as the denfity of the fluid. 



AVI, en the fame body moves through the fame fluid with 

 different velocities, this refiftance increafes in proportion 

 to the number of particles (truck in an equal time ; which 

 number is as the fpace run through in that time, that is, 

 as the velocity. But it alfo increafes in proportion to the 

 force with which the body ftrikes againft every part ; 

 which force is alfo as the velocity of the body ; and there- 

 fore, if the velocity be triple, the refiftance is triple, from 

 a triple number of parts to be removed. It is alfo triple 

 from a ftroke three times ftronger againft every particle ; 

 therefore the whole refiftance is nine-fold, that is, as the 

 fquare of the velocity. Hence, a body moved in a fluid 

 is refilled partly in a ratio of the velocity, and partly in a 

 duplicate ratio of it. 



Hence, therefore, if d denotes the denfity of the fluid, 

 11 the velocity of the body, and a and b conftant co-efficients ; 

 then a dv + iv will be proportional to the whole refiftance 

 to the fame body, moving with different velocities, in the 

 fame direction through fluids of different denfities, but of 

 the fame tenacity. But to take iiito coniideration the dif- 

 ferent tenacities of fluids, let t denote the tenacity, or the 

 cohefion of the parts of the fluid; then adv' + l>fv will 

 be as the faid whole refiftance. 



The quantity of refiftance, however, arifing from the 

 cohefion of the parts of the fluids, is very trifling with 

 refped to the other refiftance, except in very glutinous 

 ones ; and it alfo increafes in a much lower degree, being 

 only as the velocity, while the other is as the fquare of the 

 velocity. Hence then the term 1 1 v is very fmall, in refped 

 of the other term ad,v\ and, confequently, the refiftance 

 is nearly as the latter term, or nearly as the fquare of the 

 velocity : which formula has been employed by molt 

 authors, and is, indeed, very nearly the truth in flow 

 motions ; but in very rapid ones it is far from corred, not 

 fo much from the omiffion of the fmall term btv, due to 

 the cohefion ; but from the want of the full counter pref- 

 fure on the hinder part of the body, by which means a 

 vacuum, either perfed or partial, is left behind the body in 

 its motion ; and alfo perhaps to fome compreflion or ac- 

 cumulation of the fluid againft the fore-part of the body. 

 Therefore, in order to conceive the refiftance of fluids 

 to a body moving in them, it is neceflary to diftinguifh be- 

 tween thofe fluids which, being comprefl.'d by fome incum- 

 bent weight, perpetually clofe up the fpace behind the 

 body in motion, without permitting, for an inllant, any 

 vacuity to remain behind it ; and thofe fluids which, not 

 being fufficiently compreffed, the fpace left behind the 

 moving body remains for fome time empty. Thele dif- 

 ferences, in the refilling fluids, will occafion very remark- 

 able varieties in the laws of their refiftance, ami are abfo- 

 lutely neceffary to be coniidered in the determination of 

 the action of the air on fhot and fhells ; for the air partakes 

 of both thefe affedions, according to the different velocities 

 of the projected body. 



In treating of thefe refiftanccs, the fluids may likewife be 



confidered as continued or difcontinued, that is, as having 

 their particles contiguous, or as being feparated and un- 

 conneded, and alfo as either elaftic or non-elaftic. 



If a fluid was fo conftituted, that all the particles com- 

 pofing it were at fome diftance from each other, and there 

 was no adion between them, then the refiftance of a body 

 moving in it would be eafily computed, from the quantity 

 of motion communicated to thefe particles : for inftance, if 

 a cylinder moved in fuch a fluid in the diredion of its axis, 

 it would communicate to the particles it met with a velocity 

 equal to its own, and in its own diredion, fuppofing that 

 neither the cylinder, nor the parts of the fluid, were elaftic ; 

 whence, if the velocity and diameter of the cylinder be 

 known, and alfo the denfity of the fluid, there would thence 

 be determined the quantity of motion communicated to the 

 fluid, which, adion and re -adion being equal, is the fame 

 with the quantity loft by the cylinder, confequently the 

 refiftance would be thereby afcertained. 



In this kind of difcontinued fluid, the particles being 

 detached from each other, every one of them can purfue 

 its own motion in any diredion, at leaft for fome time, in- 

 dependent of the neighbouring ones ; wherefore, if inftead 

 of a cylinder, moving in the diredion of its axis, a body, 

 with a furface oblique to its diredion, be fuppofed to move 

 in fuch a fluid, the motion which the parts of the fluid 

 will hereby acquire, will not be in the diredion of the re- 

 filled body, but perpendicular to its oblique furface ; whence 

 the refiftance to fuch a body will not be eftimated from the 

 whole motion communicated to the particles of the fluid, 

 but from that part of it only which is in the diredion of 

 the refilled body. In fluids then, where the parts are thus 

 difcontinued from each other, the different obliquities of 

 that furface, which goes foremoft, will occafion confiderable 

 changes in the refiftance ; although the fedion of the folid, 

 by a plane perpendicular to its diredion, fhould in all cafes 

 be the fame. And fir Ifaac Newton has particularly deter- 

 mined, that, in a fluid thus conftituted, the refiftance of a 

 globe is but half the refiftance of a cylinder of the fame 

 diameter, moving in the diredion of its axis with the fame 

 velocity. 



But though the hypothefis of a fluid, thus conftituted, 

 be of great ufe in explaining the nature of refillances ; yet, 

 in reality, we know of no fuch fluid exifting in nature ; 

 all the fluids, with which we are converfant, are fo formed, 

 that their particles either lie contiguous to each other, or 

 at leaft ad on each other in the fame manner as if they did ; 

 confequently, in thefe fluids, no one particle contiguous to 

 the refilled body can be moved, without moving at the 

 fame time a great number of others, fome of which will 

 be diltant from it ; and the motion thus communicated to 

 a mafs of the fluid, will not be in any one determined direc- 

 tion, but will in each particle be different, according to 

 the different manners in which it lies in contad with thofe 

 from which it receives its impulfe ; whence great numbers 

 of the particles being diverted into oblique directions, the 

 refiftance of the moving body, which will depend on the 

 quantity of motion communicated to the fluid in its own 

 diredion, v. ill neceffarily be different in quantity, from 

 what it would be in the preceding fuppofition, and its elli- 

 mation becomes much more complicated and operofe. 



If the fluid be compreffed by the incumbent weight of 

 it upper parts, as all the fluids are with in, except at their 

 very furface, and if the velocity of the moving body be 

 much lefs than that with which the parts of the fluid would 

 rufh into a void fpace, in confequenc- of their compreflion ; 

 it is evident, that in this cafe the fpace left by the mo'. 

 body will be inftantaneoufly filled up by the fluid ; ami 



parti 



