On atmospheric oscillations

Abstract 1. The chief question discussed in this paper (§§ 6—12) is that of the free oscillations of an atmosphere whose temperature varies with the altitude ; and in particular the case of a uniform vertical temperature-gradient is studied in some detail. For consistency it is assumed that the expansions and contractions follow the adiabatic law. The problem is treated as a two-dimensional one, the space co-ordinates involved being horizontal and vertical; and the more definite conclusions arrived at relate to the case where the (horizontal) wave-length is somewhat large in comparison with the height of the atmosphere. The results are most easily interpreted when the temperature-gradient does not fall much below that characteristic of a state of convective equilibrium. The normal modes of oscillation then fall into well-defined types.