14 
MR. J J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
§ 9. We must now refer back to the equations of impact (§ 2). It is apparent 
that the sum of the impinging vis viva of both molecules does not alter in either 
the meeting or overtaking impact; what is gained by one is lost by the other, or 
/3-B + S 2 D = (3 0 2 B + S 0 2 D = /3i 2 B + S 1 2 D. But in every case except one a trans¬ 
ference of vis viva must take place from the one to the other. 
The exception is found in the meeting impact when /3 == 1/B and & = 1/D ; then 
shall /3 0 = (3 and § 0 = S, but at the same time /3 1 is not equal to (3, or S 1 to S ; in every 
other case /3 0 is not equal to (3 nor to (3 V nor is S 0 equal to S or to S 1 . 
It can seldom happen that the molecules strike each other directly. In taking 
account of the collective result of their fortuitous concourse we must view the position 
of the plane of concurrence and the respective inclinations of the line of motion of 
each molecule to it as three independent variables. The incident velocity of each is 
the absolute velocity resolved perpendicular to the plane, and the equations apply to 
this portion only of the vis viva of the molecules. 
Although the variety in the mode of impact is infinite, it is certain that one 
direction of motion is as likely as any other, and hence, that the opposite of any 
direction is equally probabie to the direction itself. 
Let us confine our attention to any single case of impact and suppose that the 
directions of the motions of the two impinging molecules lie on one side of the plane 
of concurrence, then it appears that the nature of the impact must be overtaking. 
Again, let us suppose that they lie similarly disposed on the other side of the plane; 
the nature of the impact is again overtaking. Now, instead of having the opposite of 
both the original lines of motion, suppose the opposite of one only is taken ; it is clear 
that the nature of the impact is in this case of the meeting kind; and the opposite 
of the other line of motion being taken while the first is in its original position, the 
impact is again of the meeting kind. 
Each of these four cases are equally probable, and the resolved velocities, or the 
values of (3 and S, are the same in all, but two are meeting impacts and two are 
overtaking, each couple having perfectly distinct numerical equations to define the 
relation between the incident and reflected vis viva. 
We are thus obliged to infer that the intestine action of the medium must be 
viewed in this manner as divided into two kinds of impacts specifically distinct in the 
numerical relation that subsists between the velocity before and after concurrence, 
and when employing the equations for summing up the results of the whole indefinitely 
great multitude that take place in mixed media, the effect of any one meeting impact 
must be considered along with its counterpart overtaking impact with the same 
velocities. 
§ 10. We have remarked that it is only the resolved portion of the whole vis viva 
of a molecule that is dealt with by the equations—that forms the force of impact— 
and it may be questioned whether the mean ol these forces in each kind of molecules 
bears the same proportion to each other as the whole vis viva of each. That the ratio 
