  The linear stability of accretion disks is revisited. The governing equations
are expanded asymptotically and solved to first order in the expansion
parameter $\epsilon$ defined by the ratio of the disk's vertical thickness to
its radial extent. Algebraically growing solutions are found for global
perturbations on the radial accretion flow of thin inviscid compressible
Keplerian disks. The algebraic temporal behavior is exhibited in the vertical
velocities and the thermodynamic variables and has the form $t\sin\Omega_0 t$
locally in the disk where $\Omega_0$ is the Keplerian rotation rate. The
physical implications and relations to the Solberg-Hoiland stability criteria
are discussed.
