Existing theories of the motion of the media in a rotary mill, and the calculation of mill power are extended to account for the actual motion of balls within a mill. A new definition of angle of repose of the charge, which is based upon fundamental properties of the shape of the charge, and remains defined over all mill speeds, is proposed. Mechanistically correct definitions of the centre of circulation and centre of mass of the charge are presented, and the usefulness of these in predicting the power draw of a mill is demonstrated. It is demonstrated that simple theories of the bulk charge motion in a mill that ignore the interaction between the layers of balls yield incorrect predictions.