Mr. R. Moon on the Impact of Compressible Bodies. 155 



motion ; and this can only be effected on the terms of a transference 

 of velocity or momentum taking place from the one cylinder, or part 

 of it, to the other cylinder, or part of it. 



lint when the cylinders are compressible, we are freed from two 

 conditions which obtain when the cylinders are rigid, 



In the first place, it is no longer necessary to suppose, neither 

 should we be justified in assuming, that the velocity abstracted from 

 each particle of the impinging cylinder, or transferred to each par- 

 ticle of the cylinder struck, is the same ; on the contrary, all expe- 

 rience tells us that, in bodies susceptible of compression, compression 

 is always produced by collision — in other words, that variation of 

 velocity, in the parts about which the collision takes place, is the 

 immediate and invariable concomitant of collision. 



In the second place, when the cylinders arc compressible, it is no 

 longer essential to suppose that the effect of the collision will be 

 to withdraw velocity from every particle of the impinging cylinder, 

 and to impart velocity to every particle of the cylinder struck. 

 Undoubtedly such may be the case if the cylinders are short, if they 

 are possessed of only a moderate degree of rigidity, and if the velocity 

 before impact of the impinging cylinder is considerable. But if the 

 cylinders be long, while the velocity of the impinging cylinder is of 

 moderate amount, the contrary may occur. The condition that the 

 cylinder originally at rest shall not oppose an immediate insurmount- 

 able barrier even to the modified motion of the other may, obviously, 

 be sufficiently satisfied if a motion of contraction is imparted by the 

 collision to a definite portion of the second cylinder. 



But when the cylinders are compressible, equally as when they are 

 rigid, the collision must cause the instantaneous abstraction of ve- 

 locity or momentum, either from the whole of the impinging cylinder, 

 or from a definite part of it, and the instantaneous communication 

 of the velocity so withdrawn, either to the whole of the cylinder 

 struck, or to a definite part of it. 



We have hitherto assumed the velocity of each particle of the im- 

 pinging cylinder to have been originally uniform. Let us now sup- 

 pose, however, that immediately before impact a counter velocity of 

 variable amount is impressed on the different parts of the impinging 

 body, so that, at the instant of impact, before taking account of the 

 effect of collision, the velocity at any point of the impinging body 

 may be expressed by V — V,, — where V is constant, but Vj has the 

 value zero at the surface of collision, and thence gradually increases 

 as we recede towards the other extremity of the cylinder, so that 

 V — V lf which expresses the velocity of the impinging cylinder before 

 impact, has its greatest value at the surface of collision, and dimi- 

 nishes as we recede therefrom. 



It is clear that, in the case we are now considering, the collective 

 momentum abstracted from the impinging cylinder by the collision 

 will be less, and finitely less, than that which was abstracted by the 

 collision in the former case, in which the velocity of each particle 

 of the impinging cylinder was supposed uniform and equal to V. 



