A discussion of the general problem of inferring fluid velocities in the core from magnetic data. Previous results are compared with one another, and the earlier analysis is extended by allowing for small contributions to secular change from magnetic diffusion, while constraining the velocity to satisfy a quasi-geostrophic condition. The latter condition is derived from first principles, and allows for electromagnetic forces in addition to the Coriolis force. The under-determined system of equations is solved by applying a variational principle which sets up the condition that nonsingular solutions correspond to a given magnetic Reynolds number. Solutions are shown for several values of the Reynolds number and for the first time include estimates of surface electrical-current patterns. 55 pp. Refs. (KB)
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