RESISTANCE. 



foremost, has its resistances, as the tan- 

 gent to an arch of a circle, whose diame- 

 ter is equal to 'the parameter, and the 

 tangent equal to half the basis of the 

 parabola. 5. The resistances of an hyper- 

 bola, or the semi ellipsis, when the base 

 and when the vertex go foremost, may 

 be thus computed ; let it be as the sum, 

 or difference, of the transverse axis and 

 latus rectum is to the transverse axis, so 

 is the square of the latus rectum to the 

 square of the diameter of a certain circle ; 

 in which circle apply a tangent equal 

 to half the basis of the hyperbola or el- 

 lipsis. Then say again, as the sum, or 

 difference, of the axis and parameter is 

 to the parameter, so is the aforesaid tan- 

 gent to another right line. And further, 

 as the sum, or difference, of the axis 

 and parameter is to the axis, so is the 

 circular arch corresponding to the afore- 

 said tangent, to another arch. This done, 

 the resistances will be as the tangent to 

 the sum, or difference, of the right line 

 thus found, and that arch last mentioned. 

 6. In general, the resistances of any 

 figure whatsoever, going- now with its 

 base foremost, and then with its vertex, 

 are as the figures of the basis to the sum 

 of all the cubes of the element of the 

 basis divided by the squares of the ele- 

 ment of the curve line. All which rules, 

 he thinks, may be of use in the fabric or 

 construction of ships, and in perfecting 

 the art of navigation universally. As also 

 for determining the figures of the balls 

 of pendulums for clocks. 



As to the resistance of the air, Mr Ro- 

 bins, in his new principles of gunnery, 

 took the following method to determine 

 it : he charged a musket-barrel three 

 times successively with a leaden ball f of 

 an inch diameter, and took such pre- 

 caution in weighing of the powder, and 

 placing it, as to be sure, by many previ- 

 ous trials, that the velocity of the ball 

 could not differ by 20 feet in 1" from its 

 medium quantity. He then fired it against 

 a pendulum, placed at 25, 75, and 125 

 i'eet distance, &c. from the mouth of the 

 piece respectively. In the first case it 

 impinged against the pendulum with a 

 velocity of 1670 feet in 1" ; in the second 

 case, with a velocity of 1550 feet in 1" ; 

 and in the third case, with a velocity of 

 1425 feet in V ; so that in passing through 

 50 feet of air, the bullet lost a velocity 

 of about 120, or 125 feet in I" ; and the 

 time of its passing through that space 

 being about _i_or'_i_ of 1", the medium 

 quantity of resistance must, in these in- 

 stances, have been about 120 times the 



weight of the ball; which, as the ball 

 was nearly -^ of a pound, amounts to 

 about 10/6. avoirdupoise. 



Now if a computation be made, ac- 

 cording to the method laid down for com- 

 pressed fluids in the thirty-eighth Propos. 

 of Lib. 2 of Sir Isaac Newton's Principia, 

 supposing the weight of water to be to 

 the weight of air as 850 to 1, it will be 

 found that the resistance of a globe of 

 three quarters of an inch diameter, mov- 

 ing with a velocity of about 16UO feet in 

 l /; , will not, on those principles, amount 

 to any more than a force of 41/6. avoirdu- 

 poise; whence we may conclude (as the 

 rules in that proposition for slow motions 

 are very accurate) that the resisting pow- 

 er of the air in slow motions is less than, 

 in swift motions, in the ratio of 41 to 10, 

 a proportion between that of 1 and 2, 

 and 1 to 3. 



Again, charging the same piece with 

 equal quantities of powder, and balls of 

 the same weight, and firing three times 

 at the pendulum, placed at 25 feet dis- 

 tance from the mouth of the piece, the 

 medium of the velocities with which the 

 ball impinged was 1690 feet in 1". Then 

 removing the piece 175 feet from the pen- 

 dulum, the velocity of the ball, at a me- 

 dium of five shots, was 1300 feet in 1". 

 Whence the ball, in passing through 150 

 feet of air, lost a velocity of about 390 

 feet in 1" ; and the resistance, computed 

 from these numbers, comes out some- 

 thing more than in the preceding in- 

 stance, amounting to between 11 and 12 

 pounds avoirdupoise : whence, according 

 to these experiments, the resisting power 

 of the air to swift motions is greater than 

 in slow ones, in a ratio which approaches 

 nearer to the ratio of 3 to 1, than in the 

 preceding experiments. 



Having thus ascertained the resistance 

 to a velocity of near 1700 feet in 1", he 

 next proceeded to examine this resist- 

 ance in smaller velocities : the pendulum, 

 being placed at 25 feet distance, was fired 

 at five times, and the mean velocity with 

 which the bull impinged was 1180 feet in 

 1". Then removing the pendulum to the 

 distance of 250 feet, the medium velocity 

 of five shot at this distance, was 950 feet 

 in 1" ; whence the ball, in passing through 

 225 feet of air, lost a velocity of 230 feet 

 in 1", and as it passed through that in- 

 terval in about ^L of I", the resistance 

 to the middle velocity will come out to be 

 near 33^ times the gravity of the ball, or 

 2/6. 10 oz. avoirdupoise. Now the resist- 

 ance to the same velocity, according to 

 the laws observed in slower motions, 



