212 Cis Reply to D. [Serr 
of B after the impulse, or the motion it acquires by the stroke 
=e Aa — as A = ck ; and in any other parallel case, the 
,! 
motion acquired by the same B at rest = a Now by the 
views in the quotations I have made from Hutton, Playfair, 
Emerson, and C. himself, it is evident that if the momenta A a 
and A’ a’ were equal, the intensities of the strokes and the 
momenta due to the body B after the strokes would be equal. 
That is — = a or A = A’,‘however unequal the value of 
A and A’ may be.” 
A moment’s consideration will show, that this apparent absur- 
dity arises from another assumption made by D. without any 
reason, by which he attributes to the writers referred to, opinions 
which he knows they do not hold, and consequences which the 
very proposition he himself ascribes to them contradicts. That 
no such inference as that which D. has drawn from the quota- 
tions is fairly deducible from them, or was intended by the 
authors, is evident, not only from the quotations themselves, but 
by what the authors have written in other parts of their works. 
For it is still true that “bodies act with a force equal to their 
momentum,” although neither the force nor momentum can 
fairly be measured by the effects of their collisions on bodies 
which yield to the stroke ; and that this was the opinion of those 
writers, D. knew at the time he attributes the contrary, not to 
the quotations only, but to their views. Thus he has said before, 
“The old theory makes the two bodies go on together; and 
hence the collision deprives the striking body of only a part, not 
of the whole of its motion.” (Annals, May, 1822, p. 358.) And 
one of the propositions which he has introduced for the purpose 
of controverting the old theory, is to show that the velocity of 
the striking body has no effect on the collision if the momenta 
are equal, (Ibid. p. 360.) Ihave already shown that the momen- 
tum of the body struck which is at rest before the stroke is 
affected by the velocity of the striking body, though other things 
are equal, but the proposition itself sufficiently proves the truth 
of the old opinions, and D.’s knowledge of them. Thus he says 
that the velocity of B after the stroke is = a and in any 
A'd B 
A’+B 
A’ a’, and B is the same in both cases; therefore, Aa B = 
A’ a’ B. If then A be greater than A’; A + B must be greater 
than A’ + B, and consequently A a B divided by the greater 
A + B must be less than A’ a’ B divided by the lesser; that is, 
— is less than -< =. When, therefore, D. states, that by the 
other parallel case, By = But the momentum A a = 
. 
