76 LECTURE VI I r. 



of inelastic bodies may be imitated by elastic ones, if we cause them to unite 

 or adhere after an impulse, so as to destroy the effect of the repulsive force 

 which tends to separate them. 



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 reassume their primitive form, and separate with a velocity equal to that 

 with which they before approached each other. Strictly speaking, the repul- 

 sion commences a little before the moment of actual contact, but only at a 

 distance which in common cases is imperceptible. 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 witli black lead, or 

 printing ink ; or by suffering it to fall from various heights : the degree of 

 compression will then be indicated 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 conveni- 

 ent 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 velocities 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 com- 

 monly divided into equal parts, although it would l^e 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 



