  In this note we calculate the Casimir effect of free thermal gravitons in
Einstein universe and discuss how it changes the entropy bound condition
proposed recently by Verlinde [hep-th/0008140] as a higher dimensional
generalization of Cardy's formula for conformal field theories (CFT). We find
that the graviton's Casimir effect is necessary in order not to violate
Verlinde's bound for weakly coupled CFT. We also comment on the implication of
this new Cardy's formula to the thermodynamics of black $p$-brane.
