332 Mr Vincent, Experiments on Impact. 



Experiments on Impact. By J. H. Vincent, D.Sc, B.A., 

 A.R.C.Sc. 



Introduction. 



Newton was one of the first who performed experiments on 

 impact. In the famous scholium on the laws of motion 1 after 

 showing that the momentum of two impinging spheres is con- 

 served he says : " In bodies imperfectly elastic the velocity of the 

 return is to be diminished together with the elastic force ; because 

 that force (except when the parts are bruised by their congress, 

 or suffer some such extension as happens under the strokes of 

 the hammer) is (as far as I can perceive) certain and determined 

 and makes the bodies to return one from the other with a relative 

 velocity, which is in a given ratio to that relative velocity with 

 which they meet." 



This number is usually denoted by e and has received the 

 name of " the coefficient of restitution." Newton found that e 

 was independent of the size and the relative velocity of the 

 spheres and thus depended only on the material of which the 

 sphere was composed. 



Hodgkinson 2 next attacked the subject. His experiments 

 were very exhaustive, and his chief result was that although e 

 was approximately constant for spheres of the same material 

 or the same two materials, yet it diminished slightly when the 

 velocity of concurrence was increased. 



Newton experimented with bodies which were not permanently 

 deformed, but Hodgkinson dealt also with bodies which suffered 

 a permanent deformation and found that the value of e in these 

 cases diminished more rapidly than in the case of bodies which 

 did not undergo any such persistent change. 



In this paper experiments on bodies which suffer large defor- 

 mation, whether permanent or temporary, are described. 



Experiments on Rubber Balls. 



Fig. 1 shows the result of a series of experiments with a lawn 

 tennis ball divested of its cloth covering. Its mass was 49 grams 

 and its diameter 6 cm. The ball was placed at different heights 

 above a stone bench or stone floor, and allowed to fall by means 

 of a light wooden lever actuated by a stretched rubber band. 



1 Motte's Principia, vol. i. p. 31. 



2 Brit. Assoc. Report, 1834. 



