30 MR. J. J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
Let P be the molecular plane consisting of (n — l) molecules, and Q one of its lower 
molecules at rest between attractive and repellent forces. 
G 
( 1 .) Let Q receive an impulse in the direction GQ, so that its initial velocity may be 
QE = v ; it will proceed along the line QA until its motion is subdued at some point 
A by the molecular repulsive force ; at the instant when the centre of gravity of the 
molecule Q, and centre of gravity of P, are at their minimum distance both move 
together with the common velocity vjn, and this is the velocity communicated to their 
common centre of gravity, which is not disturbed further by their mutual action during 
the vibratory motion that ensues. In this case there is both molecular vis viva com¬ 
municated to Q, and also the velocity vjn to the common centre of gravity, and a free 
molecule of the medium has lost the velocity v. 
( 2 .) Suppose, in the next instance, that the centre of gravity of P + Q or n to be 
stationary, while Q is continuing its vibrations, and let it be struck when at the 
centre of its descending vibration by a free molecule having the same velocity QE. 
They will be reflected from each other without gain or loss of motion, and Q will move 
back towards A instead of forward to G. Here there is a loss of the down motion 
and the gain of an up motion. By the first ( 1 .) the centre of gravity of P continues 
to ascend with the velocity- 7 that it has at the instant of impact; and as the 
J n — I 
downward force of Q that subdued this is gone, the centre of gravity of the whole 
k + Q or n molecules acquires the permanent upward velocity v/n. By the second ( 2 .) 
the same velocity vjn is given to the common centre of gravity by the gain of the up 
motion as in the first case of impact. The result of the second mode of impact is thus 
to communicate the velocity 2 v/n to the common centre of gravity. 
(3.) If the same kind of impact takes place with Q in the middle of the ascending 
vibration, it is evident that the force of impact is zero at that point, and the upward 
velocity to the centre of gravity zero. Now + Oj -p 2 (impacts) = -. This result 
is more obvious if we assume the velocity of the free molecules v fi- X and that of Q = v. 
The result of the first of these is 
2v + \ 
, and of the second - . Plalf the sum of these 
n 
