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The problem of linearized oscillations of the gaseous envelope of a rotating sphere (with periods in excess of a day) is considered using the @-plane approximation. Two particular &planes are used-one centered at the equator, the other at a middle latitude. Both forced and free oscillations are considered. With both 8-planes it is possible to approximate known solutions on a sphere. The use of either 8-plane alone, however, results in an inadequate description. In particular it is shown that the equatorial @-plane provides good approximations to the positive equiv- alent depths of the solar diurnal oscillation, while the midlatitude 8-plane provides good approximations to the negative equivalent depths. The two 8-planes are also used to describe Rossby-Haurwitz waves on rapidly rotating planets, and the vertical propagatability of planetary waves with periods of a day or longer.

PLANETARY WAVES ON BETA-PLANES