

COMPOSITION AND RESOLUTION OF FORCE. 



217 



had in common with the horse, and therefore, in leaving the point D, he has 

 two motions, expressed by the lines D F and D B. The compounded effects 

 of these motions carry him from D to C. Strictly speaking, his motion from A 

 to D, and from D to C, is not in straight lines, but in a curve. It is not neces- 

 sary here, however, to attend to this circumstance. 



If a billiard-ball strike the cushion of the table obliquely, it will be reflected 

 from it in a certain direction, forming an angle with the direction in which it 

 struck it. This affords an example of the resolution and composition of mo- 

 tion. We shall first consider the effect which would ensue if the ball struck 

 the cushion perpendicularly. 



Let A B, fig. 14, be the cushion, and C D the direction in which the ball 



Fig. 14. 

 A. 



Cr^ 1 



moves toward it. If ffie ball and the cushion were perfectly inelastic, the re- 

 sistance of the cushion would destroy the motion of the ball, and it would be 

 reduced to a state of rest at D. If, on the other hand, the ball were perfectly 

 elastic, it would be reflected from the cushion, and would receive as much mo- 

 tion from D to C, after the impact, as it had from C to D before it. Perfect 

 elasticity, however, is a quality which is never found in these bodies. They 

 are always elastic, but imperfectly so. Consequently the ball, after the impact, 

 will be reflected from D toward C, but with a less motion than that with which 

 it approached from C to D. 



Now let us suppose that the ball, instead of moving from C to D, moves 

 from E to D. The force with which it strikes D, being expressed by D E', 

 equal to E D, may be resolved into two, D F and D C'. The resistance of 

 the cushion destroys D C 7 , and the elasticity produces a contrary force in the 

 direction D C, but less than D C or D C 7 , because that elasticity is imperfect. 

 The line D C expressing the force in the direction C D, let D G (less than 

 D C) express the reflective force in the direction D C. The other element, 

 D F, into which the force D E' is resolved by the impact, is not destroyed or 

 modified by the cushion, and therefore, on leaving the cushion at D, the ball is 

 influenced by two forces, D F (which is equal to C E) and D G. Consequently 

 it will move in the diagonal D H. 



The angle E D C is, in this case, called the " angle of incidence," and C D 

 H is called the " angle of reflection." It is evident, from what has just been 

 inferred, that, the ball being imperfectly elastic, the angle of incidence must 

 always be less than the angle of reflection, and, with the same obliquity of 

 incidence, the more imperfect the elasticity is, the less will be the angle of re- 

 flection. 



In the impact of a perfectly elastic body, the angle of reflection would be 

 equal to the angle of incidence. For then the line D G, expressing the reflec- 



