290

THEORY AND PRACTICE

TRACT 37.

For the circumstances relating to the motion of a bloc!*,suspended by, and vibrating on, an axis, when struck by aball, see Tract 34, arts. 21 ... . 31.

problem six.

160 . To determine the Circumstances relating to a givenBall discharged from a Cannon, with a given Charge ofPowder.

A A

Let the annexed figure re-present the bore of the gun ;abd being the part occupiedwith the gunpowder. And put

a = ab, the length at first occupied by the charge ;

b = ae, the whole length of the gun bore;

c = *7854, the area of a circle whose diameter is 1;

d = bd, the diameter of the ball, or of the bore;

e = the specific gravity of the ball, or weight of 1 cubic

foot;

g — 16 t v or 16 feet, descended by a body in 1 second ;m — 230 oz, the pressure of the atmosphere on 1 sq. inch ;n to 1 the ratio of the first force of the fired powder, tu thepressure of the atmosphere;w= the weight of the ball; and let

x = AC, any variable distance of the ball from a, in movingalong the gun barrel. Then,

First, cd 1 is = the area of the circle b.d of the ball;therefore med 2 is the pressure of the atmosphere on bd ;conseq. mned 2 is the force of the powder on bd.

But the force of the inflamed, powder is supposed to beproportional to its density, and the density is inversely as thespace it occupies; therefore the force of the inflamed pow-der on the bail at b, is to the force on the same at c, as acis to ab ; that is,

x : a : : mned 1 : = f, the motive force at c ;

X

conseq. — f, the accelerating force there..