362 D:s Reply to C/s Observations [May, 



body striking the same with the same velocity will give it twice 

 the motion, and so the motion generated in the other will be as 

 theybrce of percussion." — (Emerson's Tracts, p. 13.) 



1 shall make no further observations on the coincidence of the 

 preceding Props, and the quotations; let C, if he can, show the 

 diiference. Let him also tell the world what he himself means 

 by the following passage in his paper. Annals for Dec. p. 421 ; 

 and let him point out which or what part of the preceding Props. 

 it refutes. " Now bodies act with a force equal to their momen- 

 tum." If C. cannot do either of these things, perhaps he will 

 have the goodness to clear up the following difficulty, or paradox, 

 which has perplexed me a little in his favourite doctrine. Let a 

 perfectly hard ball. A, moving with any velocity, a, strike in the 

 line of its motion another perfectly hard ball, B, at rest; then by 

 the old theory the motion ofB after the impulse, or the motion it 



acquires by the stroke, = A a — ^— ^ A = t— ^ ; and in any 



other parallel case the motion acquired by the same B at rest = 



° . Now by the views in the quotations I have made from 



Hutton, Playfair, Emerson, and C. himself, it is evident that if 

 the momenta A a and A' a' were equal, the intensities of the 

 strokes and momenta due to the body B after the strokes would 



be equal. That is, — — ^ = —, — g, or A = A', however une- 

 qual the values of A and Pif may be. In other words, if the 

 theory and quotations be both correct, there cannot he a number 

 greater or less than unity. Would C, the unsolicited friend and 

 voluntary champion of the old theory, be kind enough to unravel 

 this scientific enigma? I need not exhort him to embrace so 

 excellent an opportunity of displaying, without equivocation and 

 subterfuge, and without any paltry attempt to evade, the true 

 merits of the theory he professes so well to understand. As the 

 principles of the theory for which he voluntarily, I will not say 

 unnecessarily or officiously, throws down the gauntlet " are as 

 nearly as possible self-evident," it will not, I presume, require 

 any time or reflection in him to explain this matter. In next 

 month's Annals, therefore, I hope he will, for the credit of him- 

 self and theory, mathematically clear it up ; and thus expose the 

 fallacy of what, perhaps, he will readily demonstrate to be "mere 

 figments of the imagination." Should, however, a want of 

 leisure prevent his complying with my request at so early a 

 period as I have named, let him only say in the next number that 

 he will do what I require, and I will patiently wait any time that 

 he pleases. 



Prop. C. 



If a perfectly hard ball strike another perfectly hard ball at rest 



