  We have reexamined the similarity solution for a self-gravitating isothermal
gas sphere and examined implication to star formation in a turbulent cloud.
When parameters are adequately chosen, the similarity solution expresses an
accreting isothermal gas sphere bounded by a spherical shock wave. The mass and
radius of the sphere increases in proportion to the time, while the central
density decreases in proportion to the inverse square of time. The similarity
solution is specified by the accretion rate and the infall velocity. The
accretion rate has an upper limit for a given infall velocity. When the
accretion rate is below the upper limit, there exist a pair of similarity
solutions for a given set of the accretion rate and infall velocity. One of
them is confirmed to be unstable against a spherical perturbation. This means
that the gas sphere collapses to initiate star formation only when the
accretion rate is larger than the upper limit. We have also examined stability
of the similarity solution against non-spherical perturbation. Non-spherical
perturbations are found to be damped.
