1822.] on Mr, Herapath's Theory, 367 



but denies the consequence, without showing why, or assigning 

 any other reason, than that he is " at a loss to discover '' how it 

 follows. We shall, perhaps, not lose our pains in transcribing 

 what C. says on this subject; for if we can derive no informa- 

 tion, the consideration of it will afford us amusement. *^ How," 

 says C, *^ Mr. H. proves that the intensity of the stroke is the 

 force with which each of the balls is acted on in a direction 

 opposite to that in which it came at the time of the contact, 

 I am at a loss to discover J" " The intensity of the force," 

 observes C. " is equal to the sum of the momenta with which 

 both balls come in contact, half of which is one direction and half 

 in the opposite" Here C.'s mathematical refutation of Mr. H.'s 

 theory amounts to this— he cannot see how it is, nor how it is^ 

 not. But the beauty of all lies in the elegant, the decisive, the 

 irrefragable mathematical demonstration with which he esta- 

 bhshes his counter proposition. He tells us " half the intensity 

 is one direction, half in the opposite ; " and he proves it — how ? 

 — not mathematically, not by common legitimate induction; 

 but without a fact — ^without a circumstance, nay even without 

 a word either for it or against it. This mode of procedure is per- 

 fectly consistent with C.'s general method, but let me again 

 remind him that mere assertions are totally insufficient to over- 

 turn well-founded reasoning. 



'*' Jf," says C, " a man push with all his strength against a 

 wall, say with a force of 10, action and reaction being equal, the 

 wall resists with a force as 10. If, instead of the wall there be 

 an opposing active force, another person, for instance, pushing 

 against the first with an exactly equal force," '* by Mr, Hera- 

 path^s reasoningy each person would be acted on in a direction oppo^ 

 site to that toiuards which he pushed, by a force equal to tivice the 

 force of either one ; that is, with a force of 20, and consequently 

 both must be pushed backwards." These sentences, as far as I 

 understand them, distinctly charge Mr. H. with confounding 

 pressure with impulse, and with applying the laws of a single 

 impulse between perfectly hard bodies to a pressive force. 

 Flatly to contradict this, and to challenge C. to produce only one 

 expression of Mr. H. corroborative of such assertions, would be 

 to raise this attempt to depreciate and misrepresent Mr. H.'s 

 labours to an importance to which not even the best of C.'s 

 objections seems entitled. I shall, therefore, merely quote a 

 passage or two from Mr. Herapath's papers declarative of his 

 opinion on pressure and impulse ; and then leave C. to compare 

 them with his own assertions. 



" It is manifest from the drift of it," (a passage in Mr. Tred- 

 gold's attack) ** Mr. T. can compare pressure with impulse. Of 

 course, he can also compare a mathematical line with an area ; 

 and thence tell us how many lines there are in a superficies, how 

 many superficies in a solid ; and, as a finale, I expect how many 

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