[Illustration: GALILEO GALILEI (1564-1642).] Fig. 19 shows the path through the air of a ball which has been struck by a bat at the point _A_, and started off in the direction _A B_ with a velocity of 200 feet per second. In accordance with the first law of motion, if it were acted upon by no other force than the impulse given by the bat, it should travel along the straight line _A B_ at the uniform rate of 200 feet per second, and at the end of the fourth second it should be 800 feet from _A_, at the point marked 4, but during these four seconds its weight has caused it to fall 256 feet, and its actual position, 4', is 256 feet below the point 4. In this way we find its position at the end of each second, 1', 2', 3', 4', etc., and drawing a line through these points we shall find the actual path of the ball under the influence of the two forces to be the curved line _A C_. No matter how far the ball may go before striking the ground, it can not get back to the point _A_, and the curve _A C_ therefore can not be a part of a circle, since that curve returns into itself. It is, in fact, a part of a _parabola_, which, as we shall see later, is a kind of orbit in which comets and some other heavenly bodies move. A skyrocket moves in the same kind of a path, and so does a stone, a bullet, or any other object hurled through the air. [Illustration: FIG. 19.--The path of a ball.] 36. THE THIRD LAW OF MOTION.--"To every action there is always an equal and contrary reaction; or the mutual actions of any two bodies are always equal and oppositely directed." This is well illustrated in the case of a man climbing a rope hand over hand. The direct force or action which he exerts is a downward pull upon the rope, and it is the reaction of the rope to this pull which lifts him along it. We shall find in a later chapter a curious application of this law to the history of the earth and moon. It is the great glory of Sir Isaac Newton that he first of all men recognized that these simple laws of motion hold true in the heavens as well as upon the earth; that the complicated motion of a planet, a comet, or a star is determined in accordance with these laws by the forces which act upon the bodies, and that these forces are essentially the same as that which we call weight. The formal statement of the principle last named is included in--