  In this paper, we consider the volume enclosed by the microcanonical ensemble
in phase space as a statistical ensemble. This can be interpreted as an
intermediate image between the microcanonical and the canonical pictures. By
maintaining the ergodic hypothesis over this ensemble, that is, the
equiprobability of all its accessible states, the equivalence of this ensemble
in the thermodynamic limit with the microcanonical and the canonical ensembles
is suggested by means of geometrical arguments. The Maxwellian and the
Boltzmann-Gibbs distributions are obtained from this formalism. In the
appendix, the derivation of the Boltzmann factor from a new microcanonical
image of the canonical ensemble is also given.
