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Asymptotic equations describing slowly varying planetary-scale motions of the atmosphere over the rotating earth are derived and compared to the geostrophic equations of motion in the tangent plane approximation. Since the same approximation procedure is used in both the spherical and plane geometry, a direct term by term comparison is possible. The plane approximation yields familiar prognostic equations (initial value problem); but in the more constrained spherical geometry, a more restricted forcing-type problem results if the zonal motion is time-dependent. That is, with a given slowly varying or steady zonal motion, is associated a class of long-wave tesseral motions, i.e. coupled low-wave-number and meridional motions. (Author)