* v:\ 



INTRODUCTION TO MECHANICS. 



angle of incidence, the other the angle of reflection, and theSe angles are, 

 if the bodies be perfectly elastic, equal. 



We shall now explain the nature of compound motion. If a body be 

 struck by two equal forces, in opposite directions, it will not move. But 

 if the forces, instead of acting on the body in opposition, strike it in twe- 

 directions inclined to each other, at an angle of 90 degrees, if the ball 

 A (Jig. 8) be struck by equal forces at X and at Y, the force X 

 would send it towards B, and the force Y towards C ; and since these 

 forces are equal, the body cannot obey one impulse rather than the other. 

 Yet as they are not in direct opposition, they cannot entirely destroy 

 the effect of each other ; the body will therefore move, but, following the 

 direction of neither, it will move in a line between them, and reach D in the 

 same space of time that the force X would have sent it to B, and the force Y 

 would have sent it to C. Now, if two lines be drawn from D to join B and 

 C, a square will he produced, and the oblique line which the body describes 

 is called the diagonal of the square. Supposing the two forces to be 

 unequal, that X, for instance, be twice as great as Y ; then X will drive 

 the ball twice as far as Y, consequently the line A B (fig* 9) will be 



Fig. 8. Fig. 9. Fig. 10. 



twice as long as the line AC; the body will in this case move to D ; 

 and if lines be drawn from that point to B and C, you will find that 

 the ball will have moved in the diagonal of a rectangle. Let us now 

 suppose the two forces to be unequal, and not to act on the ball in 

 the direction of a right angle, but in that of an acute angle. The ball 

 will move from A to D (Jig. 10), in the diagonal of a parallelogram, 

 A B D C. Forces acting in the direction of lines forming an obtuse angle 

 will also produce motion in the diagonal of a parallelogram. For in- 

 stance, if the body set out from B instead of A, and was impelled by 

 the forces x and y, it would move in the dotted diagonal B C. 



We shall now proceed to circular motion : this is the result of the action 

 of two forces on a body, by one of which it is projected forward in a right 

 line, whilst by the other it is continually directed towards a fixed point. 

 For instance, if I whirl a ball fastened to my hand with a string, the 

 ball will have a circular motion, because it is acted on by two forces, 

 that I give it, which represents the force of projection, and that of the 

 string, which confines it to my hand. If during its motion I were 

 suddenly to cut the string, the ball would fly otF in a straight line ; 

 being released from confinement to the fixed point, it would be acted on 

 but by one force, and motion produced by one force is always in a right 

 line. When a mop is trundled the threads fly from the centre ; but 

 being confined to it at one end, they cannot part from it; whilst the 

 water they contain is thrown off in straight lines. In the same way, the 

 flyers of a windmill, when put in motion by the wind, would be driven 

 straight forward in a right line, were they not confined to a fixed point, 



