Casimir Effect of Graviton and the Entropy Bound

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.