OP PROJECTILES. 227
tity'of compound velocity, which the shell has at the pointB (168).
235. from the construction (234.) it appears;
r. That if the point F represent the vertex of acurve, F C will express the horizontal direction whichthe lhell has at that point, and the quantity of compoundvelocity, which is less than the shell can have in anyother point of the curve.
2. That the compound velocity at the point N in-creases in proportion to the distance of N from F rthat the direction of the compound velocity forms avery acute angle with the horizon, when the point Nis very near to F, is less acute in proportion as N isfarther distant from F, and becomes a right anglewhen the shell has lost its movement of impulsion jwhich in practice is alwavs greatly below the planeA B : the velocity of the projectile is then reduced tothe unequally accelerated movement of gravity.
3. That the angle formed by the direction of theshell with the horizon, approaches nearer to a rightangle, in proportion as the angle P A B is less acute:on the contrary, when the mortar is fired at a verysmall elevation, the angle formed by the direction ofthe shell and the horizon, can only become a rightangle, in a point L far distant from the horizontal lineB A.
236. The formula mV x —:—— —f (178) serves to
0 whole line J '
express the force of the shock of a shell against a plane, of whichthe inclination is given ; the application of this formulawill be rendered more familiar by the following remarks :
1. The force of the shell N increases, in proportionto its distance from the vertex F of the curve; since itscompound velocity also increases (235, No. 2): theforce of the shell at the point B being expresied by m V— m x B kf is greater than its force at the point F,because B H is greater than C F.
2- T the shell at the vertex F strike at right anglesa vertical plane, it will impinge with all the force ex-pressed by m V = m x C F; since in this cafe, the quantity
A being equal to the whole sine, the expression , a ,
whole sine
F 2 represerjts