We have shown, that in the discontinu ed fluid, which we first described, the ob liquity of the thremost surface of the moving body would diminish the resist ance ; but in compressed fluids this holds not true, at least not in any con siderable degree; for the principal resist ance in compressed fluids arises from the greater or lesser facility with which the fluid, impelled by the forepart of the body, can circulate towards its hindermost part ; and this being little, if at all, affected by the fiirm of the moving body, whether it be cylindrical, conical, or spherical, it fol lows, that while the transverse section of the body, and consequently the quantity of impelling fluid, is the same, the change of figure in the body will scarcely affect the quantity of its resistance.
The resistance of bodies of different figures, moving in one and the same me dium, has been considered by M. J. Ber noulli, and the rules he lays down on this subject are the following : 1. If an isosceles triangle be moved in the fluid according to the direction of a line which is normal to its base ; first with the vertex foremost, and then with its base ; the resistances will be as the legs, and as the square of the base, and as the sum of the legs. 2. The resistance of a square moved accord ing to the direction of its side, and of its di agonal, is as the diagonal to the side. 3. The resistance of a circular segment (less than a semicircle) carried in a direction perpendicular to its basis, when it goes with the base fbremost, and when with its vertex foremost (the same direction and celerity continuing, which is all along supposed) is as the square of the diameter to the same, less one-third of the square of the base of' the segment. Hence the resistances of a semicircle, when its base, and when its vertex go foremost, are to one another in a sesquialterate ratio. 4. A parabola moving in the direction of its axis, with its basis, and then its vertex 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 a 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 feet 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 1"; so that in passing through 50 feet of air, the bullet lost a velocity of about 120, or 125 feet in r ; and the time of its passing through that space being about 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 A. of a pound, amounts to about 101b. 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 1600 feet in 1", will not, on those principles, amount to any more than a force of Vb. 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 I to 3.