We hav expressed in linearized form the five classical coupled equations representing the rotating gas disk of a standard disk galaxy. We solve them in three limiting cases for
the gas disk (1) Infinite thickness and uniform rotation (2) Finite thickness and uniform
rotation and (3) Infinite thickness and shearing box approximating differential rotation.
We then tested the effect of a giant high velocity cloud (HVC) colliding with the disk
at velocities in excess of 100 km/sec. We find that the usual Jeans criterion for the limit
of cloud stability is modifified by the additional term arising from the effect of the HVC
collision with the gas disk. This term, which contains the velocity of the incoming cloud, and a characteristic scale for the shock front, is closely comparable in magnitude to the
original term ( the square of the product of the sound speed and the characteristic wave
number) in the static Jeans equation and also similar in magnitude to the global effect of
shear. This result shows that an HVC falling onto a disk which contains clouds close to
Jeans equilibrium will be effective in triggering cloud collapse and subsequent star formation.