  Recursion relations for orthogonal polynominals, arising in the study of the
one-matrix model of two-dimensional gravity, are shown to be equvalent to the
equations of the Toda-chain hierarchy supplemented by additional Virasoro
constraints. This is the case without the double scaling limit. A discrete time
variable to the matrix model is introduced. The discrete time dependent
partition functions are given by $\tau$ functions which satisfy the discrete
Toda molecule equation. Further the relations between the matrix model and the
discrete time Toda theory are discussed.
