424 Observations on Mr. Herapath's Theory. [Dec. 



I hardly think it is necessary to examine further the mathema- 

 tical demonstrations of the theory, it being so entirely founded 

 upon the preposition and corollaries which have been the subject 

 of the preceding observations. The next proposition, however, 

 may, perhaps, afford a few remarks. 



" If a hard ball strike another hard ball at rest in the line of 

 their centres of gravity, an exchange of state will take place ; 

 the former will remain at rest after the stroke, and the latter will 

 proceed in the same direction in which the first was moving, 

 and with the same momentum." (Annals of Philosophy for April, 

 p. 287, Prop. 3.) 



The following is the reasoning in support of this proposition, 

 rejecting that part of it which is collateral to the argument, and 

 using words iustead of algebraic signs, which offer difficulties to 

 persons unaccustomed to them. " If we suppose A (the moving 

 body), so small as to have a ratio to B (the quiescent body), less 

 than any assignable ratio, the ratio of the motion of A after the 

 stroke to the motion of A before the stroke will also be less than 

 any assignable ratio. Therefore the motion of A after the stroke 

 wiil be unassignably small ; that is, the body A will remain at rest. 

 And because the motion of A after the stroke is indefinitely 

 small compared to the motion of A before the stroke, the inten- 

 sity of the impulse will likewise be equal to the momentum of the 

 moving body A before the stroke. But since the intensity of 

 the impulse is the force acting upon the quiescent body at the 

 time of the impulse, it is also equal to the motion acquired by 

 this body. Therefore if a hard ball, 8cc." 



And this is mathematical demonstration ! This of course justi- 

 fies Mr. Herapath in that dignified condescension with which he 

 gracefully and decorously considers that former mathematicians, 

 and Sir Isaac Newton among the number, have been mistaken, 

 not so much from absolute incapacity as from want of attention; 

 and to suggest that had they imagined the consequences dedu- 

 cible from the. collision of hard bodies, they would have scruti- 

 nized it with greater care. It is wonderful how important is the 

 consequence from so simple an assertion ; because " the motion 

 of A is unassignably small, therefore it has no motion at all;" 

 that is, because a thing is unassignably small, it does not exist. 

 Beautiful reasoning! Conclusive argument! Invincible demon- 

 stration ! Having too infinitely greater force from its wholly relat- 

 ing to things (atoms and their motions) which are all unassign- 

 ably small, and, therefore, according to Mr. Herapath, which do 

 not exist. 



Again: because if A be unassignably small, its motion after 

 the stroke is unassignably small, that is, it has no motion ; 

 therefore, " if a hard ball" (having any magnitude whatever) 

 ' ■ strike another hard ball in the line of their centres of gravity," 

 its motion after the stroke would be unassignably small; that is, 

 it would have no motion. What can be more unanswerable ? 



