The stability of a horizontal layer of Boussinesq fluid, heated from below and cooled from above, rotating uniformly about the vertical in the presence of a uniform vertical magnetic field is studied for the case where the thermal diffusivity K is much larger than the magnetic diffusivity η(= 1/μσe'where μ is the magnetic permeability and σeis the electrical conductivity). The stability problem depends on the five dimensionless numbersRa, T, M, q, qb. The Rayleigh number,Ra, is a measure of the buoyancy force, the Taylor number,T, is a measure of the Coriolis force, the Hartmann number,M, is a measure of the Lorentz force andq=k/η, whileqb=Kμσb'where σbis the electrical conductivity of the boundary.