The vorticity equations for the vertically integrated momentum are derived for both the ocean and atmosphere, subject to the hydrostatic approximation, with the ocean's surface treated as a material interface. The familiar wind-stress curl is the dominant momentum exchange mechanism for large- and synoptic-scale circulations, with the air-pressure torque on the sea surface becoming of comparable importance for motion scales of the order of 102 km. The effect of the divergence of the integrated mass flux is among the larger terms of the vorticity equation for all scales of transient motion considered.