  We formulate the $c=1$ matrix model as a quantum fluid and discuss its
classical limit in detail, emphasizing the $\hbar$ corrections. We view the
fermi fluid profiles as elements of \winf-coadjoint orbit and write down a
geometric action for the classical phase space. In the specific representation
of fluid profiles as `strings' the action is written in a four-dimensional form
in terms of gauge fields built out of the embedding of the `string' in the
phase plane. We show that the collective field action can be derived from the
above action provided one restricts to quadratic fluid profiles and ignores the
dynamics of their `turning points'.
