4 
MR, S. H. BURBURY ON THE APPLICATION 
The first term on the right-hand side expresses the work which would be done 
during the process if the spheres were material points, and no collisions took place 
between them. The second term expresses the amount by which this work is 
increased by the spheres having finite diameter c and undergoing collisions. And if 
V 0 be infinite, this additional work is 
^c 3 ^T,, or f K?iT r . 
We see then that the term n/cT r in the index of e ~ hn(T + * Tr) represents work done 
against collisions in compressing the system from an infinite volume to its actual 
volume with constant T,, It is analogous to the potential y in the usual expression 
£ -mt + x). ]q might not be inappropriate to call /cT r the potential of collisions. 
In order to confirm or otherwise the above suggestion, I proceed to consider— 
4. The distribution of energy in a vertical column of gas when m equilibrium in a 
held of uniform force, the molecules being equal elastic spheres of diameter c. 
Let the column be an infinite cylinder, f the force, being parallel to its axis. 
Take a plane perpendicular to the axis as base, and let s be the height of a point 
above that plane. Then we have, with the same notation as before, 
dp/ds = — M/p 
and, as before, 
P = |(1 + K) PT,: 
Here T,. is the average per sphere of the energy of relative motion, which alone is 
concerned in p. But, in our vertical column, assume for the moment that there is no 
stream motion that need be taken into account, and, therefore, we may write T 
instead of T,., and (3) becomes 
P — 11 1 + K ) .( 3a )- 
Now k contains p as a factor by (2). But I will now assume that, not T, but 
(T+^JT, is independent of s, so that we may write (1 + k) T — 3/2 h with h constant. 
On that assumption (3) and (4) give 
P = Po*~ hWs .(5), 
where p 0 is the value of p when s = 0. # 
5. Now consider N spheres crossing the plane 5=0 with u for vertical component 
of velocity. Of these, say N — N' reach the plane s = ds without undergoing collision, 
N' will undergo collision before reaching ds. But for every collision by which one of 
the N is struck out, there will be another collision by which another sphere is 
(4), 
* See Watson’s ‘ Kinetic Theory of Gases,’ 2nd edition, pp. 56-66, 
