1822. C.’s Reply to D. 207 
hard body and plane, the change of motion in the body is the 
half of what C. admits to that in e?ther of the two moveable 
bodies.” I certainly never did admit, nor is it even plausibl 
deducible from avy thing which I have stated or admitted, that 
the change of motion in the one body is the half of that in ecther 
one of the two bodies ; but, on the contrary, I have stated, and, 
I think, proved, that the change of motion in the one body is the 
half of the change of motion in the two bodies. But D. conti- 
nues, ‘“‘ Consequently if, as C. asserts, each of the two bodies 
just lose the whole of its motion by the stroke, the body striking 
on the plane will lose only half its motion; and, therefore, after 
the stroke, it will proceed right through the fixed imperviable 
plane, with the other half motion that remains to it!” Such 
consequences and observations are quite worthy of D.’s previous 
mode of argument. 
But how the proposition, that the change of motion has the 
same ratio as the intensity of collision, “ precisely coincides 
with Mr. Herapath’s” reasoning, D. has not explained. Mr. H. 
says, “if a hard spherical body impinge perpendicularly upon a 
hard fixed plane, the body will after the stroke remain at rest 
upon the plane.” (Annals, April, 1821, p. 284.) And he also 
says : “ But if two hard and equal balls come in contact with 
equal and opposite momenta, they will separate after the stroke 
with the same velocity with which they met.” (Amnadls, Apmil, 
1821, p. 285.) In the first case, the whole motion is said to be 
destroyed ; but in the second, when the intensity of the contact 
is double, and consequently when the change of motion ought 
to be also double, there is no change at all, either in the quan- 
tity or direction of the motion. There is a change in the direc- 
tion of the balls, equal altogether to four times the effect of the 
one ball being stopped by the plane, but just as much motion 
continues in each direction as there was before the contact. 
The next extract from D.’s reply, on which it will be neces- 
sary to observe, is the following: C. says, ‘“ that the intensity 
of the stroke between two bodies moving towards opposite parts is 
equal to the sum of their momenta ; ” and, therefore, when one of 
them is at rest before the stroke, the intensity must be equal to 
the momentum of the other.’ The words in italics, D. has 
placed within inverted commas, so marking it as if an extract 
from my former paper ; yet there is no such sentence there, nor 
did I ever say any thing fairly capable of such a meaning. 
Speaking of two hard and equal balls which “ come in contact 
with equal and opposite momenta,” I said “the intensity of the 
force is equal to the sum of the momenta with which both balls 
come in contact ;” and it is a statement, of the truth of. which 
there can be no doubt ; but from that there is no rational pre- 
tence to conclude as a consequence, that “ when one of them is 
at rest before the stroke, the intensity must be equal to the 
