Motion of Projectiles. 201 



be carried for an instant in the direction of a tangent parallel to 

 HZ; after which, the recoil taking place, the body recovers by 

 degrees the velocity by which it tends to depart from the plane 

 after the same manner in which the velocity was destroyed by 

 the compression during its approach to the plane, and it will des- 

 cribe the second part RO of the curve perfectly similar to RC. 

 Lastly, when it shall have arrived at the point O, distant from 

 the plane HZ by a quantity equal to the radius /C, it will move 

 according to the tangent OT, situated like ^C; that is, the ob- 

 lique collision of a body against an inflexible and unelastic plane, 

 (friction being out of the question) takes place in such a manner 

 as to make the angle* of reflection equal to the angle of incidence, 

 these angles having for their measure the inclination to a hori- 

 zontal plane of the tangents at the extremities C, O, of the curve 

 described by the centre of the body during its compression and 

 subsequent recoil. 



316. If BD be the direction in which a body is thrown, re- 

 gard being had to gravity, this body will describe the portion 

 DC of a parabola of which BD is the tangent, until it touches 

 the plane, then, when the compression has ceased, it will describe 

 another portion SO of a parabola equal to the first and placed 

 in the same manner. 



317. Friction, moreover, contributes to the kind of motion 

 under consideration, since it occasions a rotation in the body that 

 aids it in rising above obstacles, as we have already seen. 234, 



318. We conclude what we have to say on the subject of 

 projectiles moving in an unresisting medium, with observing 

 that, since gravity draws a body downward from the direc- 

 tion given it by the projectile force, when we take aim at an 

 object in shooting or in throwing any body, we should direct 

 the sight above this object, and so much the more above it, ac- 

 cording as it is more distant, and according also to the feebleness 

 of the force employed. It is on this account that in fire-arms the 

 line of sight makes an angle with the axis of the piece, so that 

 these lines produced would meet at a point beyond the muzzle 

 toward the mark. The projectile, ball, or bullet, propelled in the 

 direction of the axis, commences its motion in a direction making 

 a greater angle with the horizon than that made by the line of 



Meek, 26 



