The purpose of this project is to model the Earth's outer core as a thick rotating spherical shell containing an inviscid, perfectly conducting fluid of constant density in the presence of a basic toroidal magnetic field. The propagation of slow hydromagnetic waves in this model is to be studied using multiple- scale asymptotic techniques. The project will emphasize the relationship between the direction of wave propagation, the spherical geometry, wave trapping and instability. Possible explanations for the westward drift of the Earth's magnetic field will be sought.