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On Incompressible Vibrations of the Stratified Atmosphere on the Flat Earth

We consider the vibrations and waves in the atmosphere under the gravitation on the flat earth. The stratified density distribution of the back ground equilibrium is supposed to touch the vacuum at the finite height of the stratosphere. We show that incompressible motions are possible to create vibrations or progressive waves with countably many time frequencies of the vibrations or speeds of the wave propagation which accumulate to 0, say, of countably infinitely many slow and slow modes.