  The boundary terms in the Hamiltonian, in the presence of horizons, are
carefully analyzed in a simple 2D theory admitting AdS black holes. The
agreement between the euclidean approach and Cardy's formula is obtained modulo
certain assumptions on the spectrum of the Virasoro's algebra. There is no
discrepancy factor "square root of 2" once the appropriate boundary conditions
are properly recognized. The peculiar features of gravity, that the on-shell
Hamiltonian is determined by boundary terms, is the reason of the mentioned
agreement.
