214 C.’s Reply to D. [Serr 
This has been so fully explained before, and is in itself so eyi- 
dentiy true, that it would not have been again repeated, but that 
the whole of the argument in support of the proposition depends 
upon an assumption of D. that if the momenta of the striking 
bodies be equal, the generating momenta and the momenta of 
the bodies struck must be also equal. I have already show 
the fallacy of those propositions and reasoning, by which D has 
attempted to prove that the velocity of the striking body has no. 
effect upon the motion of the body struck, if the momenta of the 
striking bodies are equal; but in the support of this proposition, 
D. has not rested upon them, but instead has relied upon the 
postulates before mentioned. He then proceeds, “ Let B, B’, 
be two perfectly hard and equal balls at rest, and let A, A’, be 
any two other perfectly hard balls striking respectively B, B’, 
according to the conditions of the proposition. Let also a, a’, 
be the velocities of A, A’, before the strokes, so that Aad = 
A’a’. Then it b, be the velocity of B after the strokes, and 0’ that 
of B’, we have B 6 = B’b’ and b=06’.” Upon this assumption 
that 6 = 0’ rests the whole of the reasoning supporting this pro- 
position. I have, however, already shown that this is not the; 
case unless A = A’, and consequently a = a’; for, as before 
shown, the velocity of the body struck depends upon the velo- 
city of the striking body, and consequently B 6 may differ from 
B’ b’ to any extent less than Aa. Having assumed without, 
sufficient reason as a consequence of his postulates that b = 0’, 
he proceeds to show that if it be true, and A’ has any velocity 
after the stroke, “the body A’ which cannot move faster. than 
B’, because it comes behind it, might nevertheless have a greater 
velocity in the same direction, which is absurd.” [ readily admit. 
that if it be assumed that 6 = 0b’, whatever may be the 
magnitudes of A, A’, this absurdity will follow; but this 
only shows that the assumption is not founded im truth ; 
and consequently that if A be not equal to A’, then BO shall 
not be equal to B’b’. But D. concludes, not that B 6 is not. 
equal to B’b’ unless A = A’, but that “ A, A’, must remain at 
rest after the impulses, and consequently the bodies B, B’, pro- 
ceed with the momenta A a, A’ a’, respectively.” That this con- 
clusion is not warranted by the premises is sufficiently evident 
from the preceding observations. It was not, however, possible 
that the proposition should be proved by the argument ad absur- 
dum, as no absurdity could be greater than the proposition itself 
which it was produced to prove. 
The next proposition (Prop. D) is a repetition of part of Mr.. 
Herapath’s Cor. 3, Prop. 2 (Annals, April, 1821, p. 285), with a 
little variation ofterms. ‘“‘ If two perfectly hard and equal balls 
come in contact, when moving with equal momenta in the same 
right line towards opposite parts, the intensity of the stroke as 
felt by each body in a direction opposite to that in which it was. 
moving is equal to the sum of the momenta of the two, or twice 
