  The space of all solutions to the string equation of the symmetric unitary
one-matrix model is determined. It is shown that the string equation is
equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell $\Gr$
of the Sato Grassmannian $Gr$. This is a consequence of a well-defined
continuum limit in which the string equation has the simple form $\lb \cp
,\cq_- \rb =\hbox{\rm 1}$, with $\cp$ and $\cq_-$ $2\times 2$ matrices of
differential operators. These conditions on $V_1$ and $V_2$ yield a simple
system of first order differential equations whose analysis determines the
space of all solutions to the string equation. This geometric formulation leads
directly to the Virasoro constraints $\L_n\,(n\geq 0)$, where $\L_n$ annihilate
the two modified-KdV $\t$-functions whose product gives the partition function
of the Unitary Matrix Model.
