  The linearized Navier-Stokes equations for a system of superposed immiscible
compressible ideal fluids are analyzed. The results of the analysis reconcile
the stabilizing and destabilizing effects of compressibility reported in the
literature. It is shown that the growth rate $n$ obtained for an inviscid,
compressible flow in an infinite domain is bounded by the growth rates obtained
for the corresponding incompressible flows with uniform and exponentially
varying density. As the equilibrium pressure at the interface $p_\infty$
increases (less compressible flow), $n$ increases towards the uniform density
result, while as the ratio of specific heats $\gamma$ increases (less
compressible fluid), $n$ decreases towards the exponentially varying density
incompressible flow result. This remains valid in the presence of surface
tension or for viscous fluids and the validity of the results is also discussed
for finite size domains. The critical wavenumber imposed by the presence of
surface tension is unaffected by compressibility. However, the results show
that the surface tension modifies the sensitivity of the growth rate to a
differential change in $\gamma$ for the lower and upper fluids. For the viscous
case, the linearized equations are solved numerically for different values of
$p_\infty$ and $\gamma$. It is found that the largest differences compared with
the incompressible cases are obtained at small Atwood numbers. The most
unstable mode for the compressible case is also bounded by the most unstable
modes corresponding to the two limiting incompressible cases.
