464 Mr. Herapath's Reply to Mr. Tredgold. [Dec. 



assumption was A V — Bd. Therefore the sum A V of the 

 motions after the stroke exceeds the aggregate motion AV-Bv 

 in the same direction before the stroke, by the entire motion 

 B v ; yet he intended to prove these two motions equal. 



This, the scientific world will perceive, is Mr. Tredgold's 

 grand effort, which " strikes at the root of Mr. Herapath's 

 system, and overturns all his conclusions." Let us turn to his 

 first paper in the Phil. Mag. for Aug. and I think we shall find 

 something there which will improve the specimen I have already 

 given. 



" By examining," says Mr. T. in a note p. 132, " the simple 

 case (he alludes to bodies moving towards each other with equal 

 opposite motions) when the velocities are nothing ; that is, when 

 the opposing forces are pressures ," &c. Here Mr. T. plainly tells 

 us when compared with what goes before, that two quiescent 

 bodies which do not touch, or, if he will have it so, two bodies 

 which do touch and are wholly destitute of any natural or 

 impressed tendency to approach if they could, or to change 

 their places, press each other ! But the chief merit of this pas- 

 sage is not confined to this conclusion. It is manifest from the 

 drift of it 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 

 inches in an hour. 



Again, says Mr. T. ?' If two hard bodies moving in the same 

 direction with different momenta, so that the body having the 

 greater momentum strikes the other, the sum of the momenta 

 before and after the stroke will be the same, but an exchange 

 will take place ; for after the stroke, the striking body will move 

 with the momentum of the body struck." 



Let A be the striking body, and a its velocity, B the other 

 body, and b its velocity. By Mr. Tredgold's law, B b is the 

 motion of A after the stroke ; that is, the motion of A after the 

 stroke = Aa- (A«-Bi); and so likewise the motion of B 

 after the stroke = B b + (A a — B b). Therefore when Aa = 

 B b ; that is, when the momenta before the collision are equal, 

 or the velocities reciprocally proportional to the bodies, the 

 motions, and of course the velocities, of the bodies are unaffected 

 by the collision ; and each body retains the same velocity after 

 the collision it had before. But the velocity of A must have 

 been greater than that of B before the collision, otherwise it 

 could not have overtaken and struck it ; consequently it must 

 likewise be as much greater after collision. Now if one body 

 overtake and strike another moving in the same right line, the 

 striking body must after collision have a less or cannot have a 

 greater velocity than the body struck, in consequence of its 

 beino- obliged to move behind the other. But we have shown it 

 is greater ; and it may be as many times greater as we pleas? to 



