58 LECTURE VIII. 



When two bodies approach to each other, their form is in some degree 

 changed, and the more as the velocity is greater. In general, the repulsive 

 force exerted is exactly proportional to the degree in which a body is com- 

 pressed ; and when a body strikes another, this force continues to be 

 increased until the relative motion has been destroyed, and the bodies are 

 for an instant at rest with respect to each other ; the repulsive action then 

 proceeds with an intensity which is gradually diminished, and if the 

 bodies are perfectly elastic they re-assume their primitive form, aud separate 

 with a velocity equal to that with which they before approached each other. 

 Strictly speaking, the repulsion commences a little before the moment of 

 actual contact, but only at a distance which in common cases is imper- 

 ceptible. The change of form of an elastic substance, during collision, is 

 easily shown by throwing a ball of ivory on a slab of marble or a piece of 

 smooth iron, coloured with black lead or printing ink ; or by suffering it 

 to fall from various heights : the degree of compression will then be indi- 

 cated by the magnitude of the black spot which appears on the ball. It 

 may be shown, from the laws of pendulums, that, on the supposition that 

 the force is proportional to the degree of compression, its greatest exertion 

 is to the weight of a striking body, as the height from which the body 

 must have fallen, in order to acquire its velocity, to half the depth of the 

 impression. 



For making experiments on the phenomena of collision, it is most con- 

 venient to suspend the bodies employed by threads, in the manner of 

 pendulums ; their velocities may then be easily measured by observing the 

 chords of the arcs through which they descend or ascend, since the veloci- 

 ties acquired in descending through circular arcs are always proportional 

 to their chords ; and for this purpose, the apparatus is provided with a 

 graduated arc, which is commonly divided into equal parts, although it 

 would be a little more correct to place the divisions at the ends of arcs, of 

 which the chords are expressed by the corresponding numbers. (Plate V. 

 Fig. 72.) 



The simplest case of the collision of elastic bodies is when two equal 

 balls descend through equal arcs, so as to meet each other with equal 

 velocities. They recede from each other after collision with the same 

 velocities, and rise to the points from which they before descended, with a 

 small deduction for the resistance of the surrounding bodies. 



When a ball at rest is struck by another equal ball, it receives a velocity 

 equal to that of the ball which strikes it, and this ball remains at rest. 

 And if two equal balls meet or overtake each other with any unequal 

 velocities, their motions will be exchanged, each rising to a height equal 

 to that from which the other descended. 



The effect of collision takes place so rapidly, that if several equal balls 

 be disposed in a right line in apparent contact with each other, and another 

 ball strike the first of them, they will all receive in succession the whole 

 velocity of the moving ball before they begin to act on the succeeding ones ; 

 they will then transmit the whole velocity to the succeeding balls, and 

 remain entirely at rest, so that the last ball only will fly off. 



In the same manner, if two or more equal balls, in apparent contact, be 



