OF PROJECTILES. 167

may touch the earth in the point G of the horizontal lineD F : the vertical distance K. G between the two planes,expresles the space = S passed through by the gravitatingpower, and the horizontal line DG = AK expresles thelength of the range, or the space — q passed through in thefame time by the impelling power. If the known value

KG be substituted in the formula S = 22 _iiLi-, it will give

with great precision the time / =

2 K G .

-in which

32. 18

the

shot is driven from A to K by the impelling power. Hav-ing fired several rounds, and measured the length D G ofthe-ranges, take the mean —§ (144, No. 3); and consider-ing this space as uniformly passed through, establish thefollowing proportion; the time — t, is to the space passed

through = q , as one second, is to the space = j ; which the

shot would move through in one second, if there were no re-sistance from the air; this space is termed the initial velo-

city. For example, K G = 4 feet,

. > 4 x +

then t—\/ -

32. 18

second; and suppose AL —700 feet, then

£

t

A kgV V x8

^—=1400 feet, the initial velocity fought. The initial ve-locity thus found, is not absolutely just, since the shot, fromthe moment of quitting the piece till it touch the ground atG, has been retarded by the resistance of the air. If fromthe nature of the ground, where the experiment is made,the vertical line K G be shortened, the initial velocity willbe greater, and approach nearer the truth.

148. To determine the length of the movement of im-pulsion A M, in order to deduce from it the space palledthrough by gravity; place vertically in M a butt L M N,lay the gun in a horizontal direction, or nearly so, and at Mwhere the line of direction cuts the butt, draw transversely a

L 4 horizontal