The motion of bodies in a direction parallel to an applied magnetic field and through a perfectly conducting fluid is considered. It is shown that the perturbation in the state of the fluid cannot remain small except in the particular case when the velocity U of the body is much smaller than that of the Alfvén waves in the fluid. In this case, however, the perturbation is not confined to the neighbourhood of the body, and extends to infinity inside planes which touch the body and are parallel to the undisturbed magnetic field. In addition the body experiences a drag.