. 1821 .] Mr. Herapath's Reply to Mr. Tredgdld. 465 



imagine B to be greater than A. Therefore the velocity of the 

 striking body after collision is both greater and not greater than 

 the velocity of the other. In the same way it may be shown 

 that the velocity of the body struck will after collision be both 

 Jess and not /ess than that of the other body. 



A theory that admits such conclusions as these needs no com- 

 ment on its merits. 



At p. 133, Mr. T. observes : *' If two hard bodies move in 

 opposite directions upon the same line, with different momenta, 

 the momentum after the stroke will be equal to the difference 

 of the momenta before the stroke. The body which had the 

 greatest momentum before the stroke will be at rest after it, and 

 the other body will move with a momentum equal to the differ- 

 ence of the momenta before the stroke." 



Here it is plain Mr. T. assumes the intensity of collision to be 

 equal to the greater momentum ; because if it was either less or 

 greater, this body would after collision have some motion in the 

 same or opposite direction. Therefore the opposite motion of 

 the other body contributes nothing to the intensity of the stroke, 

 which would be equally as great whether this body was at rest, 

 or moving with a momentum equal and contrary to the other. 

 Now I wish to put Mr. Tredgold to no inconvenience, but if he 

 could get some one to stand still, while he walked at a certain 

 rate up against him ; and if he could then induce the other, 

 instead of standing still, to meet him with an equal motion, I 

 think he would have a feeling experimental proof of the falseness 

 of his theory. 



Unfortunately Mr. T. has not demonstrated this theorem ; and 

 I must acknowledge I cannot see how it is derived. There is 

 also a difficulty in the theorem itself I am unable to comprehend. 

 For instance, I have shown by this theorem that the less motion 

 contributes nothing to the stroke; and this must hold good even 

 when it is but ever so trifling less than the other motion. On the 

 contrary, if it be increased to but ever so trifling a degree greater, 

 it will contribute the whole of the stroke. Surely this is a very 

 convenient transfer of power between inanimate bodies ; but on 

 what physical principles can it be explained ? How does it operate 

 in the case of equality of momenta ? In which of the bodies does 

 the power of giving intensity to collision then side? or how is it 

 divided between tliem? 



But in Case 2 of his last paper, which is precisely the present 

 theorem, Mr. T. tells U3 that the " deficiency of reaction is A V — 

 B v." Therefore as B v increases, this deficiency diminishes, 

 and the reaction itself increases. But the reaction is only the 

 counterpart and equivalent of the action ; and the action is evi- 

 dently the intensity of collision. The intensity of collision, 

 therefore, increases by a quantity equal to the less motion as this 

 less motion increases ; and is the least when this motion is the 

 least or nothing. When consequently the less motion become* 



New Series, vol. II. 2 h 



