TRACT 37.

OF GUNNERY.

263

tion of gravity, at the rate of 16 feet in the first second, andmore or less in proportion to the square of the time. Thusthen,

105. Knowing the distance of the object to be struck, atleast nearly, compute the velocity that will be given to theshot by the proposed charge of powder, or the charge thatwill be adequate to a proposed velocity. Thus having theinitial velocity, compute by prob. 11, the velocity that willbe lost by the shot in passing through the given space ofair, between the gun and the object to be struck ; which, bysubtraction, will give the velocity of the shot when it strikesthe object. Take then the mean between this and the initialvelocity, which may be accounted a medium uniform velocitywith which the shot flies through the air, from the gun tothe object. Divide then the given space or distance by thatmean velocity, both in feet, and the quotient will be thetime of the flight in seconds very nearly. Or find the timeat once, by the 11th prob. of passing over the given distance.Lastly, find the space through which a body will freely fallby gravity in that time, and it will be the required quantitynearly, which the piece must be pointed above the object,in order to hit jt. Or compute, by prob. 10, the space thebody will descend in the air, and that will be the requisiteheight to be pointed above the object, nearly.

106. For example. Suppose the distance of the object be

1000 feet, and the piece a 24 -pounder, charged with 6lb ofpowder. Then, by the last prob. as V24 : : : 1600 :

1600 Vi = 1131 = v the initial velocity. Next, by prob.11, 1131 - 231 = 900, and N ~ 1’3035, then — + 231 =660 + 231 x 891 — v the last velocity at the place of theobject; and the medium between 1131 and 891 is 1011; then

jliiT? = 1 nearly, the time of flight. But it is well

known, that the space freely descended in 1 second is 16 feet.Therefore, if the gun be pointed at a place 16 feet above theobject, it will hit i(. Or, if 1£ be divided by the distance