412 Mr. R. Moon on the Impact of Compressible Bodies. [May 28, 



In order that the moving cy Under may not be reduced to absolute rest 

 by the collision, it is obvious that the cylinder originally at rest, or a 

 portion of it, must be moved out of the way, so as to allow of the con- 

 tinuance, even in a modified degree, of the other's 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. 



But when the cylinders are compressible, we are freed from two condi- 

 tions 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 particle of the cylinder 

 struck, is the same ; on the contrary, all experience tells us that, in bodies 

 susceptible to 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 

 coUision. 



In the second place, when the cylinders are 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 velo- 

 city 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 insurmountable barrier even to the modified motion of 

 the other may, obviously, be sufficiently satisfied if a motion of contrac- 

 tion 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 velocity or mo- 

 mentum, either from the whole of the impinging cylinder, or from a defi- 

 nite 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 withdrawn, either to the whole of the cylinder struck, or to a definite part 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 impinging 

 cylinder to have been originally uniform. Let us now suppose, 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 velo- 

 city at any point of the impinging body may bo expressed by V— ; 

 where V is constant, but 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^, which expresses the velocity of the im- 



