On the Causes, Laws, &c. of Heat, &e. 261 
For, since the active force of A is AV, the intensity of the 
force on the portion of the thread next to A must be AV; and 
as the thread is perfectly inextensible, and transmits the force 
without loss, the impulsive force on B must be AV, and its 
AV 3 
momentum +> - Also, since A cannot, on account of the in- 
extensibility of the thread, communicate less than its whole 
force to B, it would remain at rest unless acted upon by some 
other force. 
Case I1.—If both the balls be suffered to fall in the vertical 
line of the thread, so that at the moment the thread is extended 
the velocity of A may be V and the velocity of B = », 
Then, the bodies being connected, in the first instant of mo- 
tion after the stroke the bodies will move with a common velo- 
city = oe 3 as is proved by writers on Mechanics. 
But, if you suppose the bodies to be disengaged, the instant 
the impulse is communicated, and freed from extraneous force, 
then, accordingly as AV, or Bu, is the greater, the velocity will 
be AYIBY. op AYSB! 
Sp ltgey Avani 
For, let AV be the greater force, then the tension of the thread 
cannot be greater than AV, unless there be a reacting force 
greater than AV; and since Bu is less than AV, the deficiency 
of reaction is AV—Bv. ‘Therefore, AV—Bvw is the momentum 
< AV—B 3 
communicated to B; or ——~—— the velocity of B. 
B 
As this conclusion does not depend on any particular velocities, 
it is true when A and B are pressures; and the principle of col- 
lision I have propounded is a general principle both in statics 
and dynamics. . 
If the momenta AV, Bu, were equal, neither of the balls would 
move in consequence of the stroke when left at liberty; for 
AV—Bv=0. 
I have done enough to show any mathematician the difference 
between the theory Mr. Herapath calls new and the old one. I 
make use of the connecting thread purely for the purpose of as- 
sisting Mr. H. in seeing that the intensity of the stroke is the 
sane in Case I. as in Case Il. when AV is the same in both. 
He is well aware that it strikes at the root of his system, as it over- 
turns the conclusions he arrives at in his Prop. V. and Prop. II. 
Cor.2. ‘ His mistake is, in making the force of contact equal to 
the sum of the momenta. The force of contact cannot be greater 
than the momentum of the striking body, for the nature of the 
opposing force contributes nothing to the stroke, be it reaction 
or momentum, 
I can 
