TRACT 37.

OR GUNNERY.

311

calculations of the same author, though extremely ingenious,-are equally erroneous, chiefly for want of a knowledge of thetrue resistance of the air, to bodies when moved with greatvelocities.

188. From what has been done in the last two articles, wecan now deduce a much more convenient theorem lor find-ing the velocity in all cases, as well as the greatest velocityCommunicated to the ball, from any given gun, and with anygiven charge of powder. In those articles, the quantitiesemployed, besides the constant numbers, are or may be allcounted in calibers of the gun ; for the diameter d is 1 cali-ber, and a and b, the length of the charge and of the gun,can be as conveniently estimated in calibers, as in any othermeasures whatever. The general theorem being

, x hyp.

, 4e;mn acd 2 , . b 64 x 230 n

V % = Arjr X -— xhyp.log.— == -T— X

12 w + J 1 ° a iv

log. — = 1226n x x hyp. log. —, or v z = 2824 n x

n a w+\W J1 ° a

ecd* . 6 , _ . w n errf 2 i b

——: x com. log. —, or v = 8473m X ^-. X com. log. —:

w + 6 a 3w + «/ ° a ’

where w denotes the weight of the iron ball, w' the weightof the powder, n the first strength of the powder, or howmany times it is stronger than the elasticity of common air,and c = '7854. But now, the diameter of the ball being d,its content will be j.cd J cubic inches, and its weight w = 4'3X | ,cd l = \ 6 cdK And the diameter of the powder being dalso, and its length a ; therefore its content is acd 1 , and itsweight - S422 5acd r . Then, substituting these values of w anda/ in the above formula, it becomes by reduction v l — 15625mX 16rf a + a X log. of 4 nearly. Or, putting the num-ber of calibers or diameters contained in a the length of thecharge, the theorem becomes it = 15625m x x °f

or® = 125 V'(y^-^ X log. of t -); being the simplestand most easy theorem for the ball’s velocity that has yetbeen found, and is besides general for all diameters andlengths of guns whatever, all the dimensions being taken incalibers or diameters of the bore only. The quantity n might

acd 1xv +