1821.] Phanomena of Heat J Gases, Gravitation, 6^'c, 283V 



For the bodies being absolutely hard, their figures do notr 

 yield to any stroke, however great it may be, and, therefore, the/ 

 shock is no sooner given at one part than it is equally felt at 

 every other; that is, supposing the stroke is given in the direc-. 

 lion of the centre of gravity. Therefore, the stroke can have nO) 

 duration, and consequently no increase or diminution of velocity? 

 can produce a difference. 



The same thing might also be proved thus : Let two unequali 

 hard balls, moving with equal momenta in opposite directions,, 

 be conceived to come in contact at the same time with the oppo- 

 site parts of another hard ball at rest, then will the intermediate:! 

 ball remain at rest, and not titubate the one way or the other,* 

 nor be any more affected than if it had not been struck at all ; 

 for since the contacts are made at the same time, if the inter- 

 mediate ball titubates, that ball towards which it moves must 

 take a longer time to give its stroke than the other, and cannot 

 have completed it until the titubation is destroyed, because, as 

 soon as the strokes are finished, the intermediate body evidently 

 becomes quiescent in consequence of the assumed equality of 

 the momenta ; but the balls being absolutely hard, their figures 

 do not yield to the stroke, and, therefore, this exterior body 

 itself, towards which the intermediate one titubates, before it 

 has finished its stroke, must, on the supposition of titubation in 

 the middle ball, have moved backwards ; that is, before it hasi* 

 finished the stroke, it must have had all its momentum destroyed,^ 

 and a new contrary one generated. But the whole stroke which> 

 the ball could give consisted in its momentum ; consequently the' 

 body must have given its entire impulse before ithaf^ completed* 

 it, which is absurd. Therefore the intermediate body does not: 

 titubate, and the strokes are made equally smart or in equal por^. 

 tions of time, or rather both strokes are made in portions of 

 time which have no duration. 



By deducing the coUision of hard from that of soft bodies, we 

 likewise arrive at the same conclusion. At the moment two soft 

 bodies come in contact, the anterior parts of the second bodyi 

 communicate motion to the posterior parts of the first body, and. 

 a shght check is given to the second. The parts of the bodies*, 

 yielding to the blow, the bodies themselves approach nearer. la' 

 the second instant another acceleration and retardation take 

 place, and the bodies approach still nearer. The same things 

 ensue in the third and succeeding instants, until at length the* 

 second body has itself lost and communicated to the first body a: 

 . sufficient degree of motion to enable it to move with the same 

 velocity which the second body has then left ; after which the 

 stroke ceases, the two bodies are at their least distance, and go 

 on together. Thus it is with the coUision of soft bodies, and 

 those whose figures are yielding, except, perhaps, that the^ 

 strokes are given in continued unceasing pressure, and not in a^ 

 succession of impulses at stated intervals; but in whichever way^ 

 it be conceived to be done, it amounts to the same thing, and* 



