TRACT 37.

OF gunnery;

265

109. Corollary. From the preceding calculation, the fol-lowing general rule is easily derived, d denoting the givendistance of the object, in feet; d the diameter of the ball, ininches, obtained from the table of weights and diameters inprob. 10; b the weight of the ball, and c that of the chargeof powder, both in pounds; v = 1600^^ the projectile ve-locity, as given in prob. IS ; v the last velocity with whichthe ball strikes the object; and t the time of the ball’s flight.Then,

Divide d by l338d, considering the quotient as a log.

Take n = the natural number of the log,Take v = + y the final velocity.

And t —

1338d

, X log. of . ~) by prob. 11.

Or t = a n approximation near enough.

• 4d*

Then, \6t z =: + - - a is the height above the object to be

pointed.

Or = — 4l> is the tangent of the angle of elevation.

D (v+t )) 1 * °

110. So that, the height of the mark to be pointed at,above the object, is nearly as the square of the distance, andthe angle of elevation simply as the distance, the projectilevelocity being the same. But, in the case of different ve-locities, the height and the angle will be reciprocally as thesquare of the velocity nearly. When once the proper anglehas been found, and verified by experience, then a dispertmay be so fixed on the gun, that the visual line may make■with the axis of the piece the proper angle. Now, as suchsmall elevations are hardly perceptible, the reason is plain,why it is thought that the ball proceeds a conflderable wayfrom the gun in a straight line. But, small as the curvatureis, when the gun is pointed horizontally, it is still smallerwhen elevated in an angle above the horizon; because, inthis case, the gravity acts obliquely on the path, or only