  The gaussian ensemble and its extended version theoretically play the
important role of interpolating ensembles between the microcanonical and the
canonical ensembles. Here, the thermodynamic properties yielded by the extended
gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range
interactions are analyzed. This model presents different predictions for the
first-order phase transition line according to the microcanonical and canonical
ensembles. From the EGE approach, we explicitly work out the analytical
microcanonical solution. Moreover, the general EGE solution allows one to
illustrate in details how the stable microcanonical states are continuously
recovered as the gaussian parameter $\gamma$ is increased. We found out that it
is not necessary to take the theoretically expected limit $\gamma \to \infty$
to recover the microcanonical states in the region between the canonical and
microcanonical tricritical points of the phase diagram. By analyzing the
entropy as a function of the magnetization we realize the existence of
unaccessible magnetic states as the energy is lowered, leading to a treaking of
ergodicity.
