1 822.] D.'s Reply to C's Observations. 35? 



Article V. 



lieplj/ to Cs Observations on Mr. Herapath's Theory . 



{Concluded from p. 296.) 



C. now sets himself about refuting Mr. H.'s theory of colli- 

 sion. A very few words will be sufficient to display on this 

 point the " distinguished excellence of C/s beautiful reasoning! 

 conchisive arguments ! invincible demonstrations ! as self-evident 

 as that two and two make five.'" C. admits that Mr. H. is cor- 

 rect in his Prop. 2, Annals for April, 1821. He allows that 

 *^ bodies act with a force equal to their momentum ; " and, there- 

 fore, as one consequence, that the force ivith which a hard fixed 

 plane and a hardball moving perpendicularly upon it come in con- 

 tact y is equal to the momentum of the ball. Again, C. grants that 

 '* the intensity of the force ivith which tioo hard balls moving in 

 opposite directions come in contact is equal to the sum of their 

 momenta." Admitting, therefore, that the three momenta in 

 these two cases are respectively equal, it is evident, by what C. 

 .himself allows to be true, that the intensity of the coUision in the 

 latter case is double the former. Now whether the changes 

 of motion be equal to the whole or only to half the intensities of 

 collision, or even to a certain part of the intensities, it is on all 

 hands allowed, I beheve, in the case of perfectly hard bodies, 

 that the changes of motion have at least the same ratio as these 

 intensities. For instance, if a certain intensity of stroke produce 

 a certain change of motion, double, treble, Sec. that intensity will 

 generate a double, treble, 8cc. change of motion. Therefore, in 

 the case of the hard body and plane, the change of motion in the 

 body is the half by what C. admits to that in either of the two 

 movable bodies. Consequently if, as C. asserts, each of the two 

 bodies just lose the whole of its motion by the stroke, the body 

 striking on the plane will lose only half its motion ; and, there- 

 fore, after the stroke, it will proceed right through the fixed imper- 

 viable plane ^ with the other half motion which remains to it ! 

 Such a consequence as this ; such a refutation of Mr. H.'s 

 theory, is well worthy the profundity of C. ; and undoubtedly 

 *^ makes it as self-evident as that two and two make five, that 

 Mr. H. has in truth quite mistaken the road to philosophical 

 science." 



It is true C. does not say that the body will pass through the 

 plane. He indeed tells us that Mr. H. is right in saying the 

 body will remain at rest on it. The conclusion, however, which 

 I have drawn is a legitimate consequence of what he grants and 

 admits ; and such 1 will venture to say that he will get no man 

 of respectable scientific ability openly to contradict. Probably 

 this reasoning meiy ^* not quadrate vvith " C.'s notion of indue- 



