OF PROJECTILES.

179

the known values of q, c, t in the formula > the

value of r will be found. For example ; let rz= 1517, andAK be found by experiment—2655, and R G—64 feet;

then r—2 ; and consequently re

7 * 2655x2

ct-q 1517X2 — 2655— 14. Having thus found the value of r for the Z2>b. shot,it way be found for the 16, 8, and ^.Ibs. from the propor-tion of the diameters of the shot (161).

164. ’she value of r being given, to find by experimentthe initial velocity of a shot fired in any direction. Supposein the first place, that when the gun is fired in a horizontaldirection A K, the first graze of the shot is at G : the lineof projection and the line of descent being known, by sub-

stituting this last value in the formula S= the

time

of flight will be found : the substitution of which in theother formula will give the value of c. For example, ifan 81b. shot be fired in the fame resisting medium as in thepreceding paragraph, r—8.8 : and supposing AKi^^Sfeet, and R G —144 feet, then 3 ; and consequently c=z

qxr + t 3478 x 8.8 + 3

-—-—-' — lZ54-

r* 8.8x3

Suppose, in the second place, (PI. 6, Fig. 18) that the gunbe fired in a direction A M, forming with the horizon theangle MAR, whose value is known ; and, that the shotstrike the ground in H : by measuring the horizontal distanceA R, the line of projection A M and the line of descentM H will be found. If M H be less than 260 feet, theinitial velocity will be greater (154), than if the gun hadbeen fired with the fame charge in a horizontal direction.Let M H=ioo feet, then t^. 2' : let A Hd —2920, and theshot be a 4 pr. fired in the same resisting medium as above,r— 7; consequently s= 1585.

165. To determine the angle of elevation (PI. 6, Fig. jgJD A F under which a shot with a charge that gives aknown initial velocity—.c will from the point A strike theobject B, above or below the horizontal line A F.

Draw the perpendicular line B D, and suppose D A to bethe direction in which the gun must be fired. Then as the

M 2 angle