1821.] Mr. Herapath's Reply to Mr. Tredgold. 463 



the hint as I wished and expected ; and though he has not per- 

 ceived in his writings what I had in view, he has nevertheless 

 replied in a manner sufficient to demonstrate, that what I said 

 could not possibly give offence to a man actuated by just and 

 peaceable feelings. Unfortunately Mr. Tredgold has taken the 

 thing in a different way. Hence there is a feeling pervading his 

 last paper in the Philosophical Magazine for October, which I 

 am sorry to perceive ; and which I the more regret to see, as 

 from the course Mr. Tredgold has thought proper to pursue, it 

 obliges me to exhibit the merits of his two papers in a light from 

 which I would willingly have kept them. 



Mr. T. in his last paper, sets out with a professed attempt to 

 demonstrate, "that in the direct collision of perfectly hard bodies, the 

 momentum before and after the stroke is the same, tvhen estimated 

 in~tke same direction." This equality of momenta, I believe, was 

 never doubted before, not only "in the direct collision of per- 

 fectly hard bodies," but in the direct or oblique collision of bodies 

 of every kind, whether perfectly or imperfectly hard, soft, or 

 elastic. In my theory, as in every other, except I suppose Mr. 

 Tredgold's, it is interwoven with the very elements ; and I have 

 re-deduced it from my results in a few instances merely to show 

 that the spirit of my inquiries has not departed from this well- 

 known principle. We shall presently see whether Mr. T. has 

 been very successful in his professed attempt to demonstrate it. 



If two perfectly hard balls, A, B, moving towards opposite 

 parts in the same right line with the velocities, V, v, strike one 

 another, then, by Mr. Tredgold's views in his last paper, if A V 

 exceed B v, the velocity of B after the stroke in a contrary direc- 

 tion to that in which it moved before the stroke is ^ — -. 



" For," says Mr. T. " the intensity of the stroke (which is his 

 tension of the thread) cannot be greater than A V, unless there 

 be a reacting force greater than A V ; and since B v is less than 

 AV, the deficiency of reaction is A V — B v. Therefore AV- 



B v is the momentum communicated to B ; or - the velo- 

 city of B." 



I cannot stop to notice as they deserve the curious paralogies 

 in these two short sentences ; I shall, therefore, merely show 

 how well this inference demonstrates the problem he intends it 

 to prove. Because A V — B v is the " deficiency of reaction," 

 it is, by Mr. T.'s account, the motion lost by A ; therefore, 

 AV— (AV— Bv) = Bz/is the motion of A after collision in 

 the same direction in which it was moving before the col- 

 lision. But Mr. T. tells us the motion of B in the same direc- 

 tion after collision is A V — B v, and, consequently, the sum of 

 these motions is A V — B v + B v = AV. Now the 

 aggregate motion in the same direction before collision by his 



