Consider a rod, at an angle to the normal of a wall,
with its centre-of-mass velocity along the normal direction,
of mass *m* and angular velocity about an
axis parallel to the wall but perpendicular to the rod. Suppose
one end of the rod, with normal component of velocity

is infinitesimally close to the wall and undergoes an instantaneous energy conserving collision; the momentum transfer from the rod to the wall can be easily found to be:

Since both and independently obey Gaussian distribution with their variances given by the equipartition of the thermal energy,

it follows, from Eq.(40), that also obeys a Gaussian distribution:

with a variance . The pressure can then be integrated to give:

which is the required result. Although derived by kinetic theory, this
result must of course correspond to that found from an appropriate
free energy derivative. Accordingly it remains applicable to rods
in solution (rather than *in vacuo*), so long as *p* is interpreted
as an osmotic pressure.

Tue Sep 17 16:40:38 BST 1996