18s

OF PROJECTILES.

angle B A F and the fide A B in the rectangled triangleB F A are known, the fides A F, B F will also be found jcall A F=m, BF~«. Since the line of descentsB Dce:

, and the line of projection AD=y

32.18^ +

», according as the point B is above or be

low F. As in the rectangled triangle AFD, AD 1 =AF‘+ DF*, by substituting the analytical values we shall have

103S* 4 +

32.i8»t"

r^ + irt + t'

the following equation

: whence may be deduced the value of t. If the pointB coincide with the point F and the butt be in the plane ofthe gun, the value of n=o, and may be struck out of theequation : the value of t being thus known, those of B Dand A D may be afterwards found, which will give the angleof elevation D A F that was sought.

166. (PI. 6. Fig. 20.) From the point B to hit the objectL situated in the same plane as the gun : the value of t maybe found in the following manner with sufficient accuracyfor practice ; since even when the amplitude of a zalb. shotis 1348 yards, the difference in the elevation HBL willnot be \ second.

The distance B L between the gun and the object, may

C T t

be considered as the line of projection q= 2nd substi-

tuting in this formula, the data y, c, r, the value of t maybe found ; which being again substituted in the formula S —

3 2 ~ gi ves the value of S for the line of descent L G :2

draw the line B G; then, in the rectangled triangle B L G,the angle GBL will be known : make the angle LBHequal to the angle GBL; B H will then be the directionin which the gun should be sired to strike the point L. Forexample, if B L be 560 yards, and a 32 pr. be fired withthe medium charge of powder, ^==1350 feet (150); andfrom the resistance of the air r~ 1 2: by substituting these

numbers in the first formula, 1680=

1350x izt

and con

12 + f

sequently