on Mr. Herapaih's Theory. 293 



in the Ime of their centres of gravity another perfectly hard 

 ball at rest. By the theories of Wallis, Wren, Huygens, and 

 Mr. Herapath, these balls will not continue together after the 

 stroke, which I think is clearly demonstrated in Mr. H.'s 3 

 Proji,, Annals for April 1821, and in my Prop. C. Annals for 

 May 1822. The theory of collision now commonly received, 

 however, which C. advocates, assumes that the balls will con- 

 tinue together after the impulse. Of C.'s attempt to prove this, 

 I have, I apprehend, fully demonstrated the failure. If he 

 fancies he can disprove what I have written, let him ; but let 

 him confine himself to direct arguments on this point ; and it 

 will then, I hope, soon be seen if C. can support liis pretensions. 

 Should he also conceive that he can pursue a better course to 

 arrive at his goal than the one he has chosen in his reply, I will 

 freely allow him to abandon the latter and to adopt any other 

 of fair mtelligible argument that he pleases. 



Modern mathematicians imagine they prove the non-separa- 

 tion of the balls after the stroke by merely telling us, that they 

 cannot separate because they are unelastic. Now what has 

 elasticity to do with absolute hardness ? Bodies, to be elastic, 

 must in the first place be soft, that is, must have a property in 

 direct opjiosition to perfect hardness. To tell us therefore that 

 two hard balls, striking one another, cannot separate because 

 they are not elastic, is to say that they cannot separate because 

 they have not a property, which can never be a concomitant of 

 perfect hardness. This is neither more nor less than giving 

 exclusivel}' to elasticity a consequence, and refusing a like ge- 

 neral consequence to hardness on the mere plea that hardness 

 is not elasticity. We should be fully as much justified in say- 

 ing, that if a body move in any direction by attraction, the 

 same or another body could not be made to move in the same 

 direction by any other means, as for instance by repulsion or 

 impulse, because neither is attraction. Any person however 

 who would gravely make the latter assertion, would run as 

 niucli risk oi being laughed at as Winston lor calculating the 

 day and hour tliat his itleal comet poui'ed from its tail the wa- 

 ters of tlie Deluge. 



What can be a more prominent proof of the absurdity of the 

 old doctrine of collision than the consecjuence it furnishes in 

 the case of two perfectly hard, equal, quiescent balls, being si- 

 milarly struck by two perfectly hard bulls having equal nu)- 

 menta? Here all the balls are supposed to be perfectly hard, 

 the quiescent bodies perfectly e(iual, the momenta which occa- 

 sion the intensities of the strokes perfectly e(]ual, and the man- 

 ner of conununicating the strokes perfectly similar ; and yel by 

 the old theory the strokes them..;elves aie ffeiicrallv une(|tial. 



If 



