The equation of balance of the absolute vorticity is derived from V. Bjerknes' Circulation Theorem, formulated in an arbitrary moving frame of general coordinates. The flux and the rate of production of absolute vorticity are defined. The case of the component of absolute vorticity normal to the equiscalar surfaces of a meteorological quantity is considered. From the expression of the horizontal convective flux of the vertical component of the relative vorticity, a relation between the horizontal meridional flows of relative vorticity and angular momentum is deduced.DOI: 10.1111/j.2153-3490.1951.tb00811.x