  The self-gravitating instability of a compressible-inviscid fluid cylinder
immersed into a self-gravitating tenuous medium of negligible motion is
developed. The stability criterion is derived based on the linear perturbation
technique. Some previous reported works are recovered. The effect of different
factors on the fluid cylinder instability is discussed. The compressibility has
a tendency for a stabilizing the model in particular as the sound speed $a$ is
very large in the stable domains $1.0233928\leq x<\infty$ but comparatively
small in the unstable domains $0<x<1.0233928$ where $x=k R_{_{0}}$ is the
dimensionless longitudinal wavenumber with $k$ is the axial wavenumber and
$R_{_{0}}$ is the radius of the cylinder. In the absence of the compressibility
factor the unstable domain is found to be $0<x<1.0678$.
