2?s THEORY AND PRACTICE TRACT 3 1 .

there seen to be '2386 and 692; therefore as 5-546: 4'403:: f 2386 : 1894 yards, the range,

: : 1 692 : 549 yards, the altitude.

That is, the range is about 1-^ mile, and the height almost •§•of a mile.

132. Again, to find the range and greatest altitude of a

9-pound ball, projected with 1500 feet velocity. The dia-meter of the 9lb ball being 4 inches, we have \Z4> : 5-546

:: 1500 -• 1766; to which in the table correspond 2343 and680 for the tabular range and altitude. Then

5'546 • 4 . ■ S 2343 : 1690 the range, almost 1 mile.

L 680 : 491 the height, almost of a mile.

133. The same table may also serve for computing theranges of mortar-shells. For this purpose, we have only tofind what must be the initial velocity of the 24-pound shotcorresponding to the proposed velocity of the shell. Thismust be deduced from the diameter and weight,of the shell,by making the velocity of the 24-pounder such, that the ra-tio of its weight to the resistance may be the same as in theshell, after the manner of the like accommodation in pro-blem 15.

Thus, to find the range of the 13-inch shell, projected withthe velocity of 2000 feet per second, at the 45° elevation.—Here, the diameter being 12 - 8 , we have j 12-8 : s / 5-546 : :2000 : 1317, and as J78 : 149-4 :: 1317 : 1105 the corre-spondent velocity of the 24-pounder; to which in the tableanswers tiie range 1930; then as 5-546 : 12-8 : : 1930 : 4455yards, or about 2 £ miles, the range.

PROBLEM XVII.

To determine the Penetrations of Balls into different' Substances.

134. The penetrations of the balls, into the blocks ofwood, formed a particular object of enquiry, in the experi-ments with the ballistic pendulum. When a body in motion