228-230] 



RESTITUTION OF FORM. 



259 



between the bodies at any instant during restitution is less than 

 that at the corresponding instant during compression in such a 

 way that the impulse of the pressure exerted during restitution is 

 the product of e and the impulse of the pressure exerted during 

 compression. On this hypothesis the impulse of the pressure 

 exerted between the two bodies while in contact is greater than 

 it would be if e were zero in the ratio 1 + e : 1. Poisson* supposed 

 this hypothetical account of the motion to apply equally whether 

 the impact is direct or not, and whether the bodies are smooth or 

 rough provided they are not sufficiently rough to prevent sliding. 



229. Coefficient of restitution. The number e is called 

 the " coefficient of restitution." For very hard elastic solids, such 

 as glass and ivory, e is little different from unity ; for very soft 

 materials, such as wool or putty, it approaches zero. The con- 

 nexion between e and the elasticity of the impinging bodies has 

 led to its being sometimes called the " coefficient of elasticity," but 

 we avoid this phrase because it has a different and very definite 

 meaning in the Theory of Elasticity. For a like reason we 

 avoid the phrase " coefficient of resilience " which has also been 

 sometimes used. Materials for which e is zero or unity may be 

 regarded as ideal limits to which some bodies approach. We shall 

 speak of such materials as being " without restitution " and " of 

 perfect restitution " respectively, ordinary materials we shall speak 

 of as having " imperfect restitution." It is, of course, to be under- 

 stood that any such phrase refers to an action between two bodies 

 of the same or different materials. The coefficient e depends on 

 both the materials just as the coefficient of friction between two 

 bodies depends on the materials and degree of polish of both. 



230. Oblique impact 

 of smooth spheres. Let 



two smooth uniform spheres, 

 of masses m, m', impinge. 



Let U, V be the resolved 

 velocities of m in the line of 

 centres and at right angles 

 thereto before impact, U' t V 

 corresponding velocities of 

 ra', and let u, v and u' y v' be 



Fig. 67. 



Traite de Mecanique, t. n., pp. 273 et seq. Second Edition, Paris 1833. 



172 



