FIRED GUN-POWDER.’ 8§

of the theorem

a=v / 9 ^ii»^A where ^ expresses the2 r

height of a barometer made of the fame metal as the shot; Ithe length of the fire-arm measured from the shot to themouth ot the piece; p the ratio between the area A S N Dand the rectangle ASx AD; and r the radius of the shot.For example, take a musquet (172) 3 ft. 8 in. in length ofbore — /; as in this ease A —2 st. 10-84 in - r = - 243 in.; and

a = 1 736 feet; suppose/>= ^2-: then by substituting these va-

lues in the theorem, 1736

/qb'SA-X 3.8 x 2.10-84 X-ff«,i73o = v/-^-*

whence « = nearly 280 times the mean elasticity of the at-mosphere.

176. The initial velocity of cannon balls may be easilyfound by this method of determining thd velocities ofbullets projected from fire-arms of small calibre: not onlythe charge that gives the longest range, and the law of pres-sure of the fluid on the shot in passing along the bare may beascertained; but the greatest elasticity of the fluid, and thepoint in the length of the bore where it is produced, may bedetermined : in a word, all the solutions of the problemsrelative to small pieces from the 167 paragraph to the present,are equally applicable to the largest cannon.

To determine the initial velocity of cannon balls, theremust be a large homogeneous butt: if necessary, one must bemade of earth, cleared of stones, sifted and well rammed.The guns must be placed near the butt, and at such a dis-tance from each other, that the loosening of the earth fromthe penetration of one shot may not facilitate the entrance ofthe other. The depth of their respective penetrations mustbe measured, and the values substituted in the place of 8 inthe theorem S=^D«‘, where D expresses the diameter ofthe shot, g it S specific gravity, and « its velocity, then

« — v ^5 which is a known quantity.

Let a wall-piece, whose initial velocity is known, besired against the fame butt; measure the penetration of the

F 3 shot