210 C.’s Reply to D. [Serr. 
rarely indeed it is, that there are not such inconsistencies in a. 
theory which is itself inconsistent with truth. 
That the difference of the velocities of hard bodies having 
equal momenta has an effect in their collision with hard quiescent 
bodies, will readily appear upon examination. Ifa hard moving 
body A, strike a hard quiescent body B, in the lines of their cen- 
tres of gravity, the quiescent body yields to the stroke, and this 
it must do lessening A’s motion, and increasing its own, until it 
shall have acquired a velocity equal to that of A. When B 
_ moves with a velocity equal to that of A, itis evident that A will 
cease to act upon it. his effect in hard bodies is produced 
instantaneously. These things being premised, and they are 
too self-evident to require further illustration, the effects of the 
difference in the velocities may be easily made evident by num- 
bers. Thus if a hard body A having a mass as 8, and a velocity 
as 6, and consequently a momentum as 48, strike in the line of 
their centres of gravity a hard quiescent body B, having also a 
mass as 8, B will not have acquired a velocity equal to that of 
A until A has communicated to it motion as 24; when both A 
and B willhave a velocity as3. But ifanother body C, having 
the same momentum as A, say 48, but having its mass as 4, and 
its velocities as 12, strike B when quiescent in a similar manner, 
B will not have acquired a velocity equal to that of C untilit has 
received motion as 32; when C and B will both have a velocity 
as 4. The quantity of motion altogether is, in both instances, 
the same after the stroke as before, there being no motion 
destroyed by the collision ; but in one case the velocity acquired 
by B is as 3; in the other as 4. In the first case after the 
stroke, the whole momentum 48 is divided by the whole mass of 
A and B, or 8 + 8 =16, making the velocity as 3, and the mo- 
mentum of B 8 x 3 = 24; in the second case, the momentum 
48 is divided by the whole mass of B and C, or 8+4=12, mak- 
ing the velocity of B as 4, and its momentum 8 x 4= 32. But 
the intensity of the stroke must be in proportion to the quantity 
of motion acquired by B, its resistance to the stroke being 
greater in proportion as it was required to attain greater velocity. 
Though, therefore, the bodies A and C, having equal momenta, 
would be capable of giving strokes of equal intensity where the 
whole motion was expended ; in the cases supposed, as the quan- 
tity of motion communicated is different, so the intensity of the 
strokes is different. 
It will sufficiently appear from the foregoing observations, that 
it was not from any difficulty in answering a similar theorem in 
Mr. H.’s paper in the Annals for April, 1820, that I passed it 
over with many others of the same kind, but because having 
shown enough to prove that the theory itself was erroneous, 1 
thought it unnecessary to trace out every error whichit contained. 
When, therefore, D. says, that ‘‘ C. descended for the purpose 
of suiting his own views to an artful omission of it,” he makes an 
