The Casimir energy for a compact dielectric sphere is considered in a novel way,
using the quantum statistical method introduced by Ho%ye and Stell and others.
Dilute media are assumed. It turns out that this method is a very powerful one:
we are actually able to derive an expression for the Casimir energy that contains
also the negative part resulting from the attractive van der Waals forces between
the molecules. It is precisely this part of the Casimir energy that has turned out
to be so difficult to extract from the formalism when using the conventional
field-theoretic methods for a continuous medium. Assuming a frequency cutoff,
our results are in agreement with those recently obtained by G. Barton.