MR. J. J. WATERSTON OR THE PHYSICS OF MEDIA COMPOSED OF 
that of its being composed of particles perfectly alike in every respect, but it is chiefly 
their identity in weight or mass that is the important point of distinction. A 
particle thus conforms to the definition that the eminent physicist Ampere has given 
to the term molecule, which we may therefore adopt as a more significant name for 
the element of a medium. 
The first department of the subject must naturally be devoted to the consideration 
of the circumstances that determine the equilibrium of such a homogeneous medium 
considered by itself. Its density, by which is to be understood not its specific gravity 
but the number of molecules in a constant volume, # may be supposed to vary without 
disturbing its homogeneity. The mean square velocity of the molecules (which in 
any infinitesimal portion of the medium may be assumed as uniform) we also have to 
consider as a variable quantity, and the physical qualities of a medium being 
dependent on these two elements of its constitution, it is necessary to determine 
clearly them mathematical relations. 
§ 2. It is evident from the definition of the hypothesis, that the medium must 
exert some expansive force on the surface that encloses it; but the nature of the 
force is not strictly continuous, it is composed of a multitude of successive sti’okes. 
Nevertheless, their succession is certainly continuous, and it is not difficult to 
conceive how they may be sufficient to counterbalance and support a superincumbent 
weight. To obtain an exact idea of this, let us suppose that a small elastic plane 
whose weight is n times that of a molecule, is supported by a regular succession of 
such molecules striking its centre of gravity with a velocity v. We seek to know T the 
condition of their mutual action when an equilibrium is maintained. 
The following are the well-known equations that express the law of elastic collision. 
They are necessarily the foundation of all reasoning on the effects of the mutual 
action of elastic bodies by impact. 
1. The Meeting Impact. 
Two molecules, B and D, meet directly in an intermediate point and strike each 
other with the respective velocities /3 and S. The velocities after impact are re¬ 
spectively 
„ n , 2(S + /3)D 
p 0 = — p -1-vm. vv— ; and 
s 0 = s- 
(B + D) 
the direction of D’s motion being reckoned positive. 
2 (8 + ft) E 
(B + D) 
2. The Overtaking Impact. 
The two molecules, B and D, with the same velocities, /3 and S, move in the same 
direction and I) overtakes B; the velocities after impact are respectively :— 
A — /3 + 
2 (S — 13) D 
and = 8 — 
2 (S — /3) B' 
(B + D) 
(B + D) 
the direction of D’s motion being reckoned positive. 
* [Attention should be directed to this use of the word “density.”—R.] 
