OP THE KINETIC THEORY TO DENSE GASES. 
3 
if u, v, w, u , v', w', be the component velocities of the two spheres. Now since nT, 
is the energy of relative motion of n spheres in volume V, 
nT, = MS 
(u — u')~ + (y — v’)~ + (w — w'Y 
in 
the summation including every pair, and therefore 
n 
SSRr = f 7rc 3 — 2nT, 
ft 
= f 7 re 3 p . 2nT„ since y = p. 
Let f 7 tc 3 p — k. Then 
SSRr = k . 2nT, for n spheres in V, 
SSRc = k . 2pT, for p spheres in unit of volume. 
Substituting this value of SSRr in (1) we obtain 
JP = t (! + x) pT, . 
It is assumed in these results that we are dealing with a space throughout which 
T, is sensibly constant. 
3. We see then that p is proportional to T, + kT,. The analogy between this 
expression and Boltzmann’s T + y, in which y denotes potential energy, suggests 
that the law of distribution of velocities among our spheres should be, instead of 
e _/,T as in the rare medium, e~ h(Tr+ xTr) , or rather, since there may be stream motion as 
well as relative motion, e ~ k<T + * Tr) . 
Let us further develop this analogy. In the Clausian equation 
f £>V = nT, + | ZZRr, 
i ^SR7- = f 7TC 3 ^ T,, 
where nT, is the kinetic energy of the motion of n spheres in volume Y relative to 
their common centre of inertia. Hence 
If the n spheres, being initially contained in volume V 0 , be compressed into 
volume Y, and T, be maintained constant during the process, the work done in 
compression is 
w = dv = { t »log a + 1 ^ (. L _ A)} IV. 
B 2 
