The flow set up in an oblate cavity of a precessing rigid body is examined under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity (ω is the angular velocity of the rigid body about the axis of symmetry, Ω is the angular velocity with which this axis precesses).

The motion of the fluid is found by considering an initial-value problem in which the axis of rotation of the spheroid is impulsively moved at a time t = 0; before that time this axis is supposed to be fixed in space, the fluid and envelope turning about it as a solid body. The solution is divided into a steady motion and transients, and, by evaluating the effects of the viscous boundary layer, the transients are shown to decay with time. The steady motion which remains consists of a primary rigid-body rotation with the envelope, superimposed on which is a circulation with constant vorticity in planes perpendicular to ω × (ω × Ω), the streamlines being similarly situated ellipses.

The possible effects of the luni-solar precession on the fluid motions in the Earth's core are discussed.