  We attempt a direct derivation of a conformal field theory description of 2D
quantum gravity~+~matter from the formalism of integrable hierarchies subjected
to Virasoro constraints. The construction is based on a generalization of the
Kontsevich parametrization of the KP times by introducing Miwa parameters into
it. The resulting Kontsevich--Miwa transform can be applied to the Virasoro
constraints provided the Miwa parameters are related to the background charge
$Q$ of the Virasoro generators on the hierarchy. We then recover the field
content of the David-Distler-Kawai formalism, with the matter theory
represented by a scalar with the background charge $Q_m=Q-{Q\over 2}$. In
particular, the tau function is related to the correlator of a product of the
`21' operators of the minimal model with central charge $d=1-3Q_m^2$.
