RESISTANCE. 



The analogy among the numbers in all thefe tables is very- 

 remarkable and uniform, the lame general law obtaining in 

 them all, by means of which, together with our preced- 

 ing remarks, we may anfwer many intereiting queilions 

 relating to this fubjtft, as connected with artillery prac- 

 tice. For example, fuppofe it were required to determine 

 what would be the refiftance of the air againft a 241b. ball, 

 difcharged with a velocity of 2000 feet per fecond. By 

 Table III. the ball of 1.965 inch diameter, when mov- 

 ing with 2000 feet velocity, fuffered a refiftance of 981bs. ; 

 then fince the refiftances, with the fame velocity, are as the 

 furfaces, and the furfaces as the fquares of the diameters; alfo 

 the diameter of a 24-pound ball being 5.6 inches, we have as 

 (1.965)'; (5.6) 1 , or as 3.86 : 31.36:: gSlbs. : 7961bs., the 

 refiftance which a 241b. ball experiences when difcharged 

 ■with the above velocity. And generally, if the diameter of 

 any propofed ball be d inches, and r the tabular refiftance 

 correfponding to any velocity v ; then we ihail generally 



have as (1.965)* : d'~ :: r 



rd' rd- , 



; ; — — = — — , or very nearly 



(1.965)^ 3.8' 



\rd>. 



Thefe refiftances relating to certain and determinate velo- 

 cities, a principal objeft of inveftigation has been, amongft 

 experimentalifts, to determine fome rule or formula by which 

 the refiftance may be found for any velocity whatever, and 

 the refult of Dr. Hutton's inveftigations on this fubjedl is 

 as follows, viz, 



Refiftance = r = .00002576 v~~ — .003S8 v, in avoir- 

 dupois pounds, the velocity being v. 



This rule .00002576 ir — .00388 <v = r denotes the re- 

 fiftance for a ball whofe diameter is 1.965 inch, the fquare 

 of which is 3.9 or 4 nearly. Hence to adapt it to any other 

 ball, whofe diameter in inches is d, we fhall have, by the fame 



d 2 - 

 proportion as above, — - (.00002576 tr — .00388 v) = 



(.00000667 *»' — .0010) d l = (.00000 -, v* — .001 11) d', 

 for the refiftance of any ball whofe diameter is d, and velo- 

 city v. 



In fmaller velocities the fame author finds the theorem 

 .00001725 v* — r fufficiently correft, and this is adapted 

 to a bail whofe diameter is d in exactly the fame manner, 

 giving the refult .00000447 d' v z = r for the refiftance 

 when the velocities are fmall. 



For the application of thefe theorems to the folution of 

 certain problems connected with the do&rine of projectiles, lee 

 that article : and for various other formulas and refults 

 equally curious and interefting, fee Di". Hutton's Tratts, 

 as alfo vol. iii. of his Courfe of Mathematics ; Robins' Gun- 

 nery ; Moore's Theory of Rockets ; Gregory's Mechanics ; 

 and Prony's Architecture Hydraulique. 



Resistance, Different, of the fame Medium to Bodies of 

 different Figures. — Sir Ifaac Newton (hews, that if a globe and 

 a cylinder, of equal diameters, be moved with equil velocity 

 in a thin medium, confiding of equal particles, diipoled at 

 equal diftances, according to the direction of the axis of the 

 cylinder ; the refiftance of the globe will be lefs by half than 

 that of the cylinder. 



Resistance, Solid of the leajl. — From the laft propoiition 

 the fame author deduces the figure of a folid which fhall 

 have the leaft refiftance of any containing the fame quantity 

 of matter and furface. 



The figure is this. Suppofe D N F G (Plate XXXVI. 

 Mechanics, fig. 15. ) to be fuch a curve, as that if from any 

 point N be let fall a perpendicular N M to the axis A B ; 

 snd from a given point G be drawn a right line G R pa- 



rallel to a tangent to the figure in N, and cut the axis, 

 when continued, in R ; M N be to G R as G R cub. to 

 4BR x GRy; a folid defcribed by the revolution of this, 

 figure about its axis A B, moving in a medium from A to-, 

 wards B, is lefs refifted than any other circular folid of the 

 fame area, &c. 



This theorem, which fir Ifaac Newton has given without 

 a demonftration, has been demonftrated by fevcral mathema- 

 ticians, as Fatio, Craig, M. d'Hofpital, Bernouilli, &c. 

 (See Dr. Horfiey's edition of Newton, vol. ii. p. 390, and 

 Maclaurin's Fluxions, feft. 606 and 607.) For a more par- 

 ticular inveftigation of this folid, feeprob. 6. under the article 



ISOI'ERIMETKV. 



Resistance of a Globe perfectly hard, and in a medium 

 whofe particles are fo too, is to the force with which the 

 whole motion may either bedeftroyed, or generated, which 

 it has at the time when it has defcribed four-thirds of its 

 diameter, as the denfity of the medium to the. denfity of the 

 globe. Hence, alfo, lir Ifaac Newton infers, that the re- 

 fiftance of a globe is, cateris paribus, in a duplicate ratio of 

 its velocity. Or its refiftance is, ceteris paribus, in a dupli- 

 cate ratio of its diameter ; or, ceteris paribus, as the denfity 

 of the medium. Laftly, that the actual refiftance of a globe 

 is in a ratio compounded of the duplicate ratio of the velocity, 

 and of the duplicate ratio of the diameter, and of the ratio 

 of the denfity of the medium. 



In thefe articles the medium is fuppofed to be disconti- 

 nuous, as air probably is : if the medium be continuous, as 

 water, mercury, &c. where the globe does not ftrike imme- 

 diately on all the particles of the fluid generating the refift- 

 ance, but only on thofe next it, and thofe again on others, &c. 

 the refiftance will be lefs by half: and a globe in fuch a me- 

 dium undergoes a refiftance which is to the force with whicli 

 the whole motion it has after defcribing eight-thirds of its 

 diameter, might be generated, or taken away, as the denfity 

 of the medium to the denfity of the globe. 



Resistance of a Cylinder, moving in the direction of its 

 axis, is not altered by any augmentation or diminution of 

 its length ; and therefore is the fame with that of a circle of 

 the fame diameter, moving with the fame velocity in a right 

 line perpendicular to its plane. 



The refiftance of a cylinder, moving in an infinite non-elaf- 

 tic fluid, arifing from the magnitude of a tranfverfe feftion, is 

 to the force with which its whole motion, while it defcribes 

 four times its length, may be taken away, or generated, 

 as the denfity of the medium to that of the cylinder, very 

 nearly. 



Hence, the refiftance of cylinders moving lengthwife, 

 in infinitely continued mediums, are in a ratio compounded 

 of the duplicate ratio of their diameters, the duplicate ratio 

 of their velocities, and ratio of the denfity of mediums. 



The refiftance of a globe, in an infinite non-elaftic medium, 

 is to the force by which its whole motion, while it defcribes 

 eight-thuds of its diameter, might be either generated or 

 taken away, as the denfity of the fluid to the denfity of the 

 globe, quant proxim-. 



Resistance of Matter. (See Matter.) The meaning 

 of this expreffion is not, that matter makes any oppo- 

 sition to a change of its ftate, or exerts a force to maintain 

 itfelf in the ftate it is, as fome have very improperly 

 expreffed themfelves. This would imply that activity which 

 is inconfiftent with its nature ; and if it were true, a part 

 of the force of every impulfe would be fpent merely in 

 overcoming this oppofition, without producing any other 

 effect ; ^nd, therefore, the fum of the motions the fame way 

 would always be greater before than after collifion, which is 

 impoflible. The largejl body will be moved by any the 



Jllght^Jl 



