132 On the Causes, Laws, &e. 
i only notice this, because Mr. Herapath seems to consider the 
doctrine of repulsion a necessary part of the received theory*. 
I come now to examine the propositions. In the first prop. 
I grant that the duration of the shock or stroke of perfectly hard 
bodies is independent of their initial velocities. If smartness be 
used as synonymous with ete I assent to the whole prop., 
bat not otherwise. 
By the Cor. I understand that the intensity of the shock i is as 
the momentum of the striking body. 
I object to the second prop. because it requires us to assume the 
existence of an object absolutely immoveable: such a thing does 
not exist, and it is not necessary to determine the laws of colli- 
sion. But in preference to refuting particular parts of Mr. Hera- 
path’s theory of the collision, I will briefly lay down what I 
conceive to be the true theory of the collision af hard bodies. 
If a body A moving with a momentum M have all its motion 
destroyed by the resistance of another body B; then the mo- 
mentum 2 of the resisting body B, must be equal to M.; that 
is, in the equilibrium of moving bodies M =m. This Mr, 
Herapath will grant; and therefore, when A strikes B, B being 
at rest, the reaction m of B, necessary to destroy the motion of 
A, will be equal to M; consequently B will move with the mo- 
mentum M, and A remain at rest. 
If the bodies meet with equal momenta, the whole motion 
will be destroyed, and the bodies will remain at rest. 
The intensities of the strokes must be equal in the two eases, 
all the difference being that motion is produced by the reaction 
in one case, and it is destroyed in the other by the same re- 
action t. 
Mr. Herapath wiil also see that the momentum coi mannieeeal 
to a hard fixed plane, at the moment of contact, will be equal to 
that of the impinging body; for it is impossible to destroy mo- 
mentum by mass alone, or by fixing. 
If two hard bodies moving in the same direction with different 
momenta, so that the body having the greater momentum strikes 
the-other, the sum of the momenta before and after the stroke 
will be the same, but an exchange will take place; for after the 
stroke, the striking body will move with the momentum of the 
body struck. 
If the body struck be at rest before the stroke, the striking 
body will be at vest after it, as we have seen before. 
* Annals of Philosophy for April 1821, p. 281. 
7 By examiping the simple case when the velocities are nothing ; that 
is, when the opposing forces are pressures, we find wherein the mistake is 
made. The inte nsity of a pressure cannot he doubled. by the mode ef op- 
posing it. See Newton's 3d Law of Motion. if 
a ee ee eee ee a a 
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