  A simple result for the pressure of a hard sphere fluid that was developed
many years ago by Rennert is extended in a straightforward manner by adding the
terms that are of the same form as the Rennert's formula. The resulting
expression is moderately accurate but its accuracy does not necessarily improve
as additional terms are included. This expression has the interesting
consequence that the pressure can have a maximum, as the density increases,
which is consistent with the freezing of hard spheres. This occurs solely as a
consequence of repulsive interactions. Only the Born-Green-Yvon and Kirkwood
theories show such a behavior for hard spheres and they require a numerical
solution of an integral equation. The procedure outlined here is ad hoc but is,
perhaps, useful just as the popular Carnahan-Starling equation for the hard
sphere pressure is also ad hoc but useful.
