TRANSACTIONS OF THE SECTIONS. 537 



ticity in the two cases being -71 and '76, or nearly equal. In 

 experiments 6 and 60, balls of brass, varying in weight as 80 

 to 1, were struck against the same stone ball, and their elas- 

 ticities varied only from '62 to '68. 



Various other proofs, both of this and the preceding " Con- 

 clusion," may be obtained from the tabulated results ; and 

 therefore the elasticities given in the tables will apply, what- 

 ever be the relative or absolute weights of the impinging 

 bodies. 



Conclusion 6. In impacts between bodies differing very 

 much in hardness, the elasticity with which they separate is 

 nearly that of the softer body. 



This may be shown by many examples : thus, lead, the elas- 

 ticity of which is '20 (Exp. 13.), is much harder than cork, 

 whose elasticity is '65 (Exp. 25.) ; but the elasticity of lead 

 struck against cork is '57, differing only ^ from that of cork 

 (Exp. 44.). The elasticities of steel, cast iron, stone, and 

 glass, are '67, -73, -79, -94, (Expts. 30, 20, 27, 24) ; and these 

 bodies are very hard, compared with lead, whose elasticity is 

 •20 ; but if they be successively struck against lead, the re- 

 sulting elasticities will be -19, -17, -28, '25 (Expts. 50, 49, 56, 

 32) ; differing not widely from that of lead. There is fre- 

 quently, however, a considerable loss of elasticity in impacts 

 between bodies differing much in hardness, arising from the 

 softer body being crushed with the blow, in the manner that a 

 soft body would be by a hammer. 



Conclusion 7. In impacts between bodies whose hardness 

 differs in any degree, the resulting elasticity is made up of the 

 elasticities of both ; each body contributing a part of its own 

 elasticity in proportion to its relative softness or compressibility. 



From Conclusion 6 we see that if any body, as lead, be struck 

 successively by two other bodies, as cork and steel, one very 

 soft and the other very hard compared with itself, the lead in 

 the first case will contribute scarcely any of its elasticity, the 

 cork giving nearly the whole of its : and in the second case the 

 lead would contribute nearly all its elasticity, and the steel 

 scarcely any. (Expts. 13, 25, 30, 43, 50.) Hence we may 

 conclude that if the lead had been struck against another body 

 of equal softness or compressibility with itself, the lead would 

 have contributed half of its own elasticity, and the other body 

 half of its own, to form the resulting elasticity. 



This reasoning seems to be borne out by experiment, as will 

 be seen further on. Admitting it therefore to be generally 

 correct, we see that in the two extreme cases of collisions, be- 

 tween bodies of equal hardness and of vert/ different hardness, 



