14 
ON THE APPLICATION OF THE KINETIC THEORY TO DENSE GASES. 
and therefore T v /T = (1 + k) j(n + k ), which increases as k increases, that is, 
cceteris paribus , as the diameter c increases. 
Again, the pressure per unit of area on a plane moving with the stream, and 
therefore the mean pressure, is p — f (1 -MpT,, which is independent of the 
diameter c. 
Now, the spheres being material points with T,. = 3/2 h, the mean pressure is 
fpT,.; that is, as we may write it, f (1 + k) pT r , because in this case k = 0. As 
the spheres increase in diameter with (1 -j- k) T r unaltered, the mean pressure per 
unit of area remains unaltered. In other words, it is exactly as much diminished by 
the conversion of part of the energy of relative motion of contiguous spheres into 
energy of stream motion as it is increased by the introduction of the term SSPtr as 
the spheres acquire diameter c. 
Comparing the actual value of p with what it would be if, with the same total 
kinetic energy, the spheres were material points, we see that it is diminished in the 
proportion 1 + k : L. 
The number of collisions per unit of volume and time is proportional to c 2 T,.; that 
is, to k*/(1 -J- k). It is less in the proportion 1 / (1 + k) than it would be if, with 
the same total kinetic energy, the spheres had velocities independent of one 
another. 
21 . From the fact that p is independent of k, it follows that local variations of 
density, i.e., of k, do not involve the expenditure of any work on the whole, and 
therefore such variations ma}^ and will come into being. 
22. Boltzmann’s minimum function continues to diminish by collisions, finally 
attaining its minimum constant value when the distribution of velocities defined by 
our assumption in 13 is established, but its actual value when minimum differs by 
h log D from what it would be if the spheres were material points. 
