This paper gives the theory of the motion of a finitely conducting, viscous liquid between long, concentric, rotating cylinders under a radial magnetic field in the case of high Hartmann number. Because the current and vorticity contents of a Hartmann layer are related, it is easy to predict the behaviour in both steady and unsteady states. Experiments with mercury which confirm the theory closely are described. As these were developed for an educational film on magnetohydrodynamics, they have the attraction that the results are immediately obvious to the observer.