TRACT 37.

OF GUNNERY.

S9l

+ r t c * . . r . 2g:mnacd* x ■

Hence, bv forces, vv == 257# = - - X —;

' * •~' y to x

the fluent of which is v 1 — x hyp. log. of x.

But, when v = o, then x = a ; therefore, by correction;tr _ *.mnacd ^ hyp. log. — is the correct fluent; conseq.

v = v/ ( ^x hyp. log. -^)istheveloc. of the ball ate; or

v ~ '- ’* x hyp. log. is the velocity rvith which

the ball issues from the muzzle at e; where h denotes thelength of the cylinder filled with powder ; a being the lengthto the hinder part of the ball; which will be more than hwhen the ball does not touch the powder;

But, the content of the ball being- Zed 1 , its weight is w —

w, j, . r ,4tzmnhcd? 6gmnh 96.2S0.144n/i

i«l 3 e; therefore V- - = 4 /—— = J --=

3 w de y ■ de

1733 Consequently the rule is

v = 1783 v'f — x hyp. log. £) = 2706v/(^ X com. log. ^).

When the ball is of cast iron, e = 7400, and the rule isv = 31'45 x log. for the velocity of the iron ball.

Or, when the ball is of lead, then e = 11325, andv = 25 , 42v'(^r X log. -^ ) for the velocity of the leaden ball;in which two theorems, a, b, d, h, may be taken in any mea-sures, either feet or inches, &c.

161. Exam. For an example, it has been found that the

medium velocity of the gun n° 2, with a charge of 4 ouncesof powder, has been about 1180 feet. Now, the ball being1 - 96 inches in diameter, and the charge of powder with itscontaining bag occupying 3 45 inches of the cylinder, but thepowder alone only 2 - 54; the numeral values of the lettersin the theorem v = 31-45 x log. ~), will be a = 3-45,

b ■= 38-43, d — l - 96, h = 2-54 ; and if We suppose n= 1000,as assumed by Mr. Robins; these substituted in that theorem,give v = 1159, being about 21 feet too little.

162. Such then is the solution of the problem in its most

V 2