“Then I will give you the reason,” said his father. “A stone projected into the air is acted upon by no less than three forces; the force of projection, which is communicated to it by the hand or the sling; the resistance of the air through which it passes, and which diminishes its velocity without changing its direction; and the force of gravity, which ultimately brings it to the ground. Now, since the power of gravity and the resistance of the air will always be greater than any force of projection we can give a body, the latter must be gradually overcome, and the body brought to the ground; but the stronger the projectile force, the longer will those powers be in subduing it, and the farther will the body go before it falls. A shot fired from a cannon, for instance, will go much farther than a stone thrown from your hand. Had the two forces which acted upon the stone, viz. those of projection and gravity, both produced uniform motion, the body must certainly have descended through the diagonal; but since gravity, as you have already learned, is an accelerating force, the body is made to describe a curve instead of a straight line. “This law, however, will require the aid of a diagram for its explanation. Let X represent the ball at its greatest altitude, X Y the force of gravity drawing it downward; and X Z that of projection. We have here, then, two forces acting in the direction of the two sides of a parallelogram. In passing on to Z, the ball will perform the diagonal X _a_; and in the next equal space of time, will descend through _three_ times the distance Z _a_, and will consequently be found at _b_; while in the next period it will fall through _five_ equal spaces, and pass to _c_; and in the next period, again, as it must fall _seven_ such spaces, it will reach the ground at _d_, having described a portion of a curve from X to _d_, or during the time that the two forces were in simultaneous operation. The same principle will explain the curved ascent of the ball, substituting only the laws of retarded for those of accelerated motion; for it is clear, that the body during its _ascent_, will be retarded in the same degree in which it was accelerated during its _descent_.” [Illustration: Fig. 9. Diagram of a parabolic flight path.] “Your explanation,” said Louisa, “appears very clear and satisfactory.” “The curve which _Projectiles_ (that is to say, bodies projected into the air) describe, is termed a _Parabola_ (16), although the resistance of the air, which is not recognised in the theory, produces a considerable influence on the practical result.”