[260° "'] 
LVII. A Refutation of Mr. Herapatu’s Mathematical In- 
quiry into the Causes, Laws, &&c. of Heat, Gases, Gravita- 
tion, &e, 
Is Mr. Herapatu’s a work, which, like the crrric OF PURE REASON, “ con- 
sists of one chain of closely-connected reasoning, and must therefore be 
wholly comprehended, or no part of it can be understood ?” 
Remark of « Disciple of Kant. 
To Alexander Tilloch, LL.D. &c. 
Sir, — Ix the last Number of the Annals of Philosophy, I am 
charged with propounding a “ new theory of collision,” in your 
Number for August, without demonstration. Whether it be ac- 
tually new, or not, I have not leisure to inquire; and perhaps it 
would be less trouble to establish its truth than to seek for other 
demonstrations to refer to. I am perfectly aware that it is not 
the same part of the theory of collision as that which generally 
fiads a place in treatises on Mechanics; consequently, I feel a 
wish to place it before your readers. 
The method I propose to take is different from that of pre- 
ceding writers; but a new view of the subject may be more satis- 
factory than an old one. / 
The proposition I have in part to demonstrate, is, that iz the 
direct collision of perfectly hard bodies the momentum before 
and after the stroke is the same, when estimated in the same 
direction. 
Let the bodies be perfectly hard spheres, A and B, and let 
these bodies be connected by a perfectly inextensible thread, 
passing over a pulley, so that the movement of the weights is 
not affected in any manner whatever by the friction, resistance, 
or inertia of the connecting apparatus. 
Case 1. Let the ball B be supported at rest, 
and lift the ball A in a vertical direction, till, 
when suffered to fall, its velocity at the extent 
of the thread is V. 
Then, because the thread is perfectly inexten- 
sible, the velocity will be communicated to B in- 
stantaneously and without loss. 
The bodies being connected, they would move 
in the first moment after the stroke with a com- 
5 AV : ; 
mon velocity = AaB} 2 is proved by writers 
on Mechanics. 
But, if you suppose A to be disengaged in the 
same instant that it transmits the impulse to B, 
then the initial velocity of B after the stroke will be 
AV 
—_—— 
Ez 
