TRACT 37.

OF GUNNERY.

255

And, as 2' ! : 5-546 1 : : av* : 7-69av' 1 = -0002041® 2 = bv 1 sup-pose, the resistance due to the same velocity with the 24lbball. Therefore = /, and — vv = 32 fx = ±bv z x, and

x = the correct fluent of which is ~ X h. 1. — = -^r

4 bit 4b v 4b

178 on

x h. 1. - = -x h. l.~ = 3674 X -171148 = G29 the

10U 4* 73

velocity sought, nearly the same as before.

PROBLEM XII.

To determine the Ranges of Projectiles in the Air.

92. To determine, by theory, the trajectory a projectiledescribes in the air, is one of the most difficult problems inthe whole course of dynamics, even when assisted by all theexperiments that have hitherto been made on this branch ofphysics; and must still be accounted such, in the full extentof the problem. Even the solutions of Newton, of Bernoulli,of Euler , of Borda, &c, &c, after the most elaborate investi-gations, assisted by all the resources of the modern analysis,amount to no more than distant approximations, that arerendered nearly useless, even to the speculative philosopher,from the assumption of a very erroneous law of resistancein the air, and much more so to the practical artillerist, bothon that account, and from the very intricate process of cal-culation, which is quite inapplicable to actual service. Thesolution of this problem requires, as an indispensable datum,the perfect determination by experiment of the nature andlaws of the air’s resistance at different altitudes, to balls ofdifferent sizes and densities, moving with ail the usual de-grees of celerity. Unfortunately however, hardly any ex-periments of this kind have been made, excepting thosewhich have been printed in the preceding Tracts of thesevolumes; which, though so extensive and varied, I cannotyet undertake to pronounce that they are fully adequate tothe purpose of all the demands, cither of the practical artil-lerist, or the speculative philosopher.