  We show that a rigidly rotating, homogeneous ellipsoid of revolution threaded
by a uniform, coaxial magnetic field is a possible figure of equilibrium. While
the spheroidal shape is fully preserved, the rotation rate is modified.
Accordingly, we extend the fundamental formula by Maclaurin. In contrast with
the non-magnetic case, prolate shapes are permitted, but there are critical
states in the form of maximum elongations, depending on ionisation fraction,
ion/electron drift, magnetic field and mass-density. As checked from numerical
simulations based on the Self-Consistent-Field method, prolate states survive
to gas compressibility. The relevance to interstellar clouds is outlined.
