The axisymmetric flow of fluid, confined within a rapidly rotating annulus and caused by a horizontally applied temperature gradient, is discussed under the assumptions of small thermal Rossby number and small Taylor number. It is initially assumed that the transfer of heat is purely conductive, and the flow is calculated for when the upper fluid surface is either rigid or free. The analysis of the problem in which the upper surface is rigid is extended so as to allow con-vective as well as conductive transfer of heat.