1822.) C.’s Reply to D. 209 
struck by two other perfectly hard balls moving with equal 
momenta, the intensities of the strokes are equal.” (Prop. A. 
Annals, May 1822, p. 260). The only material part of the rea- 
soning by which this proposition is attempted to be supported is 
the following: “All the bodies being absolutely hard, the 
strokes are mere impulses which are begun and finished with the 
very commencement of the contacts, and are, therefore, equally 
smart with respect to duration under every velocity. Hence the 
velocities of the moving bodies have no effect on the intensities 
of the strokes.” Mr. H. has stated in the Annals for April, 
1821, p. 284, “that all the strokes between perfectly hard 
bodies have no duration, and are thence equally smart.” If this 
be true, as it undoubtedly is, the strokes are eyually smart with 
respect to duration under every momentum, and consequently it 
may, with just as much reason, be concluded, that the momenta 
of moving bodies have no effect on the intensities of the 
strokes. 
But if the two similar hard balls which are supposed to be 
struck, instead of being quiescent, were moving with equal velo- 
cities, then Mr. H. himself does in a proposition which D. has 
adopted (Annals, April, 1822, p. 294), in effect clearly admit, 
that notwithstanding the strokes would be equally smart with 
respect to duration, yet the velocities of the striking bodies 
would have an effect upon the intensities of the strokes. “ If,” 
say they, “a hard body overtake and strike another hard body 
moving with less velocity in the same right line, the first body 
will after the stroke continue its course with the same velocity 
which the other body had before, and the second body will 
acquire from the stroke a momentum equal to the difference of 
the velocities of the bodies drawn into the mass of the first 
body.” According to this proposition, ifa hard body A, with a 
mass as 4, and a velocity as 6, that is, with a momentum as 24, 
overtake another hard body B, with a mass as 5, and a velocity 
as 3, B will acquire a momentum by the stroke =6—3 x 4=12. 
But if the body B moving with the like velocity be overtaken by 
another body, C, having the same momentum as A, but having 
its mass as 2, and its velocity as 12, the momentum gained by B 
will be 12—3 x 2=18. In D.’s proposition, the bodies which 
receive the stroke are supposed to be quiescent, and in that of 
Mr, H. they are supposed to be moving; that difference, how- 
ever, cannot affect the argument of D, which is founded solely 
upon the fact that the strokes are equally smart with respect to 
duration, and this is alike in both cases. I do not, however, 
allow that Mr. H.’s proposition is correct, further than as it 
admits that the difference in the velocities of bodies having equal 
momenta has an effect in the collision of hard bodies; but it 
serves to show the inconsistencies in the theory itself, and very 
New Series, vou. 1v. Pp 
