1822.] OH Mr. Herapalh's Theory. 361 



sities would be equal. And by the demonstration of this same 

 proposition, it appears, that because all the bodies are perfectly 

 hard, and the two quiescent bodies perfectly equal, and the 

 strokes similarly given, the intensities of the impulses are due to 

 the momenta alone. But other things being alike, causes are 

 proportional to their effects ; and the effects of the momenta in 

 this case are the intensities of the impulses. The intensities, 

 therefore, are proportional to the momenta. 



Cor. — Because the unconstrained changes of motioii are pro- 

 portional to the intensities of the impulses, the changes of 

 motion both in the bodies striking and bodies struck, are propor- 

 tional to the momenta. 



Before I proceed further, it will be needful, in order to ease 

 C.'s mind of apprehension, to show him that the preceding Props, 

 are perfectly compatible with the notion introduced into his 

 favourite, but little understood, theory of coUision. This I shall 

 do by a few quotations. " The force of percussion is the same as 

 the monientum or quantity of motion, and is represented by the 

 product arising from the mass or quantity of matter moved, mul- 

 tiphed by the velocity of its motion ; and that without any 

 regard to the time or duration of action ; for its action is consi 

 dered totally independent of^ time, or but as for an instant, or an 

 infinitely small time." — (Button's Mathem. Dictionary, vol. ii. 

 p. 169.) 



- " Bodies that have equal quantities of motion have equal 

 forces or equal powers, to produce motion." — (Playfair's Outhnes 

 of Nat, Philos. vol. i. p. 32.) 



'* The momentum, or quantity of motion, generated by a single 

 impulse, or any momentary force, is as the generating force." — 

 (Hutton's Courses, vol. ii. p. 132.) In the same page the same 

 writer says : *' The velocities being equal, a double mass will 

 strike with a double force ; a triple mass with a triple force ; and 

 so on." 



These quotations not only confirm the two preceding Props, 

 but the first confirms the principles on which they are founded ; 

 namely, the evanescent continuance of the strokes. What makes 

 it the more extraordinary is, that these are two of the principal 

 authors whose works C. wants to oppose to Mr. Herapath. 



M'Laurin's Fluxions, in which I believe his views of collision 

 are expounded, I have not by me. If I had I should probably 

 be able to give another amusing specimen of C.'s knowledge of 

 names instead of things ; but 1 will now beg leave to make one 

 more quotation from another of our mathematicians, whose 

 honest opinion in this matter may be entitled to some attention, 

 even if it be not supported by the discovery that Newton in 

 his theory of heat " has quite mistaken the road to philoso- 

 phical science." 



** if a body striking another gives it any motion, twice that 



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