RESISTANCE. 



fame laws by which, in the preceding cafe, the heavier body 

 defcended, as Hated in the preceding part of this article. 

 RE^tAVCZoftbeAir,mPiuumaliefiiHtie£6rce with which 



the motion of bodies, particularly of projediles, is retarded by 

 the oppofition of the air or atmofphere. See Gunnery. 



The air being a fluid, the general laws of the refiftance of 

 fluids obtain in it, except that the different degrees of denfity, 

 in the different ftages or regions of the atmofphere, occalion 

 fome irregularity. 



As to the refiftance of the air, it has been thus deter- 

 mined from experiments. Mr. Robins, in his New Prin- 

 ciples of Gunnery, chap. 2. prop. 2, &c. having taken a 

 mufket barrel, and charging it fucceffively with a leaden 

 hall of three-quarters of an inch diameter, and about halt 

 its weight of powder, and taking fuch precaution in weigh- 

 ing 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, fired it againlt 

 a pendulum, called the balliftic pendulum, (defcnbed under 

 Gunnery), placed at 25 feet, at 75 feet, and at 125 feet 

 diftance from the mouth of the piece refpe&ively. In the 

 firft cafe, it impinged 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 1" ; fo that in paffing through 50 feet of air, 

 the bullet lofl a velocity of about 120 or 125 feet in 1"; 

 and the time of its palling through that fpace being about 

 ,'-~d or 7 V,th of 1", the medium quantity of refiftance muft, 

 in thefe inftances, have been about 120 times the weight of 

 the ball ; which, as the ball was nearly V.th of a pound, 

 amounts to about iolbs. avoirdupois. 



Now, if a computation be made, according to the method 

 laid down for comprefied fluids, in the 38th propof. of 

 lib. ii. of fir 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 refiftance 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 4^-lbs. avoirdupois ; whence we may conclude, 

 the rules in that propofition for flow motions being very 

 accurate, that the refilling power of the air in flow motions 

 is lefs than in fwift motions, in the ratio of 4,1 to 10, a pro- 

 portion 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 nearly that of 1690 feet in 1". Then removing 

 the piece 175 feet from the pendulum, the velocity of the 

 ball, at a medium of five (hots, was that of 1300 feet in 1". 

 Whence the ball, in pafling through 150 feet of air, loft a 

 velocity of about 390 feet in 1"; and the refiftance, com- 

 puted from thefe numbers, gives fomething more than in the 

 preceding inftance, amounting to between 1 1 and 1 2 pounds 

 avoirdupois : whence, according to thefe experiments, the 

 refilling power of the air to fwift motions is greater than in 

 flow ones, in a ratio which approaches nearer to the ratio ot 

 3 to 1 , than in the preceding experiments. Next, to examine 

 this refiftance in imaller velocities, the pendulum being 

 placed at 25 feet diftance, was fired at five times, with an 

 equal charge each time, and the mean velocity with which 

 the b?ll impinged, was that of 11 80 feet in 1". Then re- 

 moving the pendulum io the diftance of 250 feet, the me- 

 di.im velocity of five (hot, at this diftance, was that of 950 

 feet in 1" ; whence the ball, in pafling through 225 feet of 

 air, loft a velocity of 230 feet in 1", and as it pafl'ed through 

 that interval in about Y'.ths of 1", the refiftance to the middle 



locity will com? out to be near 33^ times the gravity of 



the ball, or 2lb. iooz. avoirdupois. Now the refiftance 

 to the fame velocity, according to the laws obferved in 

 flower motions, amounts to T vths of the fame quantity ; 

 whence, in a velocity of 1065 feet in 1" (the medium of 1 180 

 and 950), the refilling power of the air is augmented in no 

 greater proportion than that of 7 to 1 1 ; whereas, in greater 

 degrees of velocity, as before, it amounted very nearly to the 

 ratio of I to 3. 



By other experiments, it appears, that the refiftance of 

 the air is very fenfibly increafed, even in fo fmall a velocity 

 as that of 4.C0 feet in 1". 



That this refilling power of the air to fwift motions is 

 very fenfibly increafed beyond what fir Ifaac's theory for 

 flow motions makes it, feems hence to be evident. It 

 being, as has been faid, in mufket, or cannon Ihot, with 

 their full charge of powder, nearly three times the quantity 

 afligned by that theory. 



However, this increafed power of refiftance diminifhes as 

 the velocity of the refilled body diminifhes, till at length, 

 when the motion is fufliciently abated, the actual refiftance 

 coincides with that fuppofed in the theory. 



The refiftance of a bullet of three-quarters of an inch 

 diameter, moving in air with the velocity of 1670 feet in 1", 

 amounting,as we faid, to iolbs., the refiftance of a cannon ball 

 of 2,j.lbs., fired with i61bs., or its full charge of powder, and 

 thereby moving with a velocity of 1650 feet in 1", (which 

 fcarcely differs from the other), may hence be determined. 

 For the velocity of the cannon ball being nearly the fame as 

 the mufket bullet, and its furface above 54 times greater, it 

 follows that the refiftance on the cannon ball will amount 

 to more than 54olbs. which is nearly 23 times its own weight. 



Euler has ihewn, that the common doftrinc of refiftance 

 anfwers very well when the motion is not very fwift, but 

 in very fwift motions it gives the refiftance lefs than it 

 ought to he, on two accounts. 1. Becaufe in very quick 

 motions the air does not fill up the fpace behind the body 

 faft enough to prefs on the hinder parts, that the refiftance 

 on the fore part is increafed. 2. The denfity of the air 

 before the ball, being increafed by the quick motion, will 

 prefs more ftrongly on the fore part, and, being heavier 

 than in its natural ftate, will retard its motion. 



He has alfo (hewn, that Mr. Robins has reftrained his 

 rule to velocities not exceeding 1670 feet in 1"; whereas, 

 had he extended it to greater velocities, the refult muft have 

 been erroneous : as he apprehends that it is not perfectly 

 exaft, when the motion is not extremely fwift. He has in- 

 veftigated a formula for determining the degree of this re- 

 fiftance, and deduced conclufions differing from thofe of 

 Mr. Robins. See Principles of Gunnery invelligated, &c. 

 1777, p. 224, &c. 



Mr. Robins having proved that, in very great changes 

 of velocity, the refiftance does not accurately follow the 

 duplicate proportion of the velocity, lays down two pofi- 

 tions, which may be of confiderable lervice in the practice 

 of artillery, till a more complete and accurate theory of 

 refiftance, and the changes of its augmentation, may be 

 obtained. The tirll of thefe is, that till the velocity of the 

 projectile furpalles that of 1100 feet in a fecond, the re- 

 finance may be eftecmed to be in the duplicate proportion 

 of the velocity : and the fecond is, that if the velocity be 

 greater than that of 1100 or 1200 feet in a fecond, the 

 abfolute quantity of the refiftance will be nearly three times 

 as great as it (hould be by a companion with the Imaller 

 velocities. Upon thefe principles, he proceeds in approxi- 

 mating the actual ranges of pieces with fmall angles of 

 elevation, -viz. fuch as do not exceed 8° or io'\ which he 

 fetsdown in a table, compared with their eorrefponding poten- 

 tial ranges. See his Mathematical Trads, vol. i. p. 1 79> & c - 

 E 2 Since 



