318

THEORY AND PRACTICE

TRACT 37.

also have a numeral value given to it: for, though the valueof n be a little various, for the different charges and guns,being between the numbers 1700 and 2300 in the last deter-mination of them in art. 174. But as that statement of thos.evalues of n, was the result of experiments made with thecharges of powder put into bags, which renders the lengthof the charge always considerably more than the real lengthwhich the powder alone would occupy in the gun cylinder,especially in the lower charges; and as the theorem, whichis just above given, supposes a to denote the length of thepowder alone, without any including bag; it may thereforebe best to take a medium among the values of n for the high-est charge, as shown in the last line of the table in the de-termination above referred to, which numbers, for the fourguns, run from 2075 to 2300, the medium among the fourbeing nearly 2200, the square root of which is 47 very nearly.This then being substituted for y'w in the last theorem, itbecomes finally v — 5875 * l°g- °f ^ or t ^ le ve "

locity of the ball in all cases, both accurate, and in its mostsimple form. Or it may ber= 5875 v'Xjg " X log. of ^),counting both a and b as expressed in calibers of the gun.

189. We shall now apply this formula in calculating thegreatest velocity of shot discharged from all guns, in a seriesof all the lengths, differing by 2 calibers at a time, with therespective length of the charges that communicate the great-est velocity; the results, with the correspondent data, arearranged in the foliovring table, which are all the same,whatever the caliber or diameter may be; the powder putin close to the plane or flat bottom of the bore, without abag, and the diameter of the ball equal to the caliber of thegun, or as nearly so as possible, with very little or no wind-age.