1822.] C.’s Reply to D. 213 
old theory, B v after the stroke is 2 a , and in parallel cases = 
A+B 
‘ 
aes he must have known that the writers who supported it 
did not think the momenta due to the body B after the strokes 
would be equal. It was, however, unnecessary in order to show 
the mode by which this difficult paradox was raised, to do more 
than refer to the paragraph itself; where he ventures to attribute 
to Hutton, Playfair, and Emerson, the belief that when A a = 
45 AaB A‘a'B 
A a, then AsB = A+B’ 
that is, that Hutton, Playfair, and Emerson, believed that equal 
quantities divided by unequal quantities produced equals. 
The next proposition is the one stated by Mr. Herapath in the 
Annals for April, 1821, p. 287, with its form a little altered. “If 
a perfectly hard ball strike another perfectly hard ball at rest in 
“the line described by the centre of gravity of the former, the 
striking body will remain at rest after the impulse, and the other 
will proceed im the same right line in which the former was 
moving, and with the same momentum.” 
“ From this,” Mr. H. has himself stated, “ it follows that a 
body in a state of free and perfect quiescence, however small it 
might be, will destroy the motion of another body however large, 
and however great its momentum.” Whether or not such pro- 
positions are not self evidently untrue, 1 must leave to the judg- 
ment of your readers; it is certainly impossible to exaggerate 
them. It will not, however, be difficult to show the fallacy in 
the reasoning offered in support of this proposition, nor will it, I 
apprehend, occasion surprise that it should be found to rest on 
assumptions as unfounded as those which have already been 
exposed. 
** All that I require,” says D, “for demonstrating this pro- 
position is, that the intensity or force of percussion be the same as, 
or equal to, the motion generated ; and that the api of percussion 
be proportional to the generating momentum. ithout adverting 
to the preceding propositions, each of these postulates is admit- 
ted in the quotations I have made from the authors C. has quoted 
against Mr. Herapath.” I have already made some observations 
on the meaning which D. has endeavoured to apply to those 
quotations, which are equally applicable to the postulates said 
to be deduced from them, upon which the reasoning in support 
of this proposition rests. For the generating momentum must 
evidently be the momentum which generates motion; that is, 
the momentum expended in producing motion, and consequently 
when the body struck yields to the stroke, the generating mo- 
mentum will not be the whole momentum of the striking body. 
Although, therefore, the momenta of the striking bodies may be 
equal, the momenta expended in producing motion in other 
bodies at rest ; that is, the generating momenta, may be unequal. 
however unequal A may be to A’; 
