240 MOTION OF SYSTEMS OF PARTICLES 



After the moment of greatest compression, a second system of 

 forces must come into play to set up the velocities with which the 

 bodies separate from one another. In fact, at the instant of great- 

 est compression, the compressed parts of the bodies act like a com- 

 pressed spring, and we can suppose the velocities of separation 

 produced by the action of this imaginary spring. The forces which 

 separate the bodies may again be treated as impulsive, and the 

 component of this impulse along the common normal will be 

 denoted by I'. The impulse /' is called the impulse of restitution. 



196. When the motion of the bodies before impact is known, we 

 can calculate the velocities at the instant of greatest compression 

 by an application of the principle of conservation of momentum. 

 It is therefore possible to calculate the impulse J, the impulse 

 of compression. 



The amount of the impulse /', on the other hand, depends on 

 the nature of the contact between the two bodies ; for instance, 

 if the bodies are perfectly inelastic, there is no separation at all 

 after impact, so that /' = 0. In general, it is found as a matter 

 of experiment that the impulse I 1 is connected with the impulse 



/ by the simple law 



I'=el, 



where e is a quantity which depends only on the nature of the 

 contact between the two surfaces, and not on the amount of the 

 impulse I. The quantity e is called the coefficient of elasticity for 

 the two bodies. 



It is important to understand that this coefficient of elasticity is a quan- 

 tity entirely different from the coefficients or elastic constants which occur 

 in the theory of elastic solids. Indeed, the term coefficient of elasticity is 

 somewhat unfortunate as a description of the quantity e ; what is measured 

 is resilience rather than elasticity, and doubtless coefficient of resilience would 

 be a better description than coefficient of elasticity. The term coefficient of 

 elasticity has, however, been generally adopted. 



197. The value of e, as we have seen, is zero for perfectly in- 

 elastic bodies. For iron impinging on lead, the value of e is about 

 .14, for iron on iron about .66, and for lead on lead about .20. We 



