  We consider the oscillations of the atmosphere around a stratified back
ground density and entropy distribution under the gravitation on the flat
Earth. The atmosphere is supposed to be an ideal gas and the motion is supposed
to be governed by the compressible Euler equations. The density distribution of
the back ground equilibrium is supposed to touch the vacuum at the finite
height of the stratosphere. Considering the linearized approximation for small
perturbations, we show that time periodic oscillations with a sequence of time
periods which accumulate to infinity, say, slow and slow oscillations, so
called `g-modes', can appear when the square of the Brunt-Vaisala frequency is
positive everywhere for the considered back ground equilibrium.
