In this Bureau of Mines study, an equation is derived for the limit burning velocity for divergent, spherical propagation from an ignition kernel of radium, r:(su)e=2a/r pu/pb. For flame propagation into a preexisting, stretching velocity gradient of magnitude dv/dx, the limit velocity is (su)e=(a dv/dx)1/2. These formulations are shown to be equivalent to the fluid dynamic concepts of damkohler, karlovitz, and markstein. Existing data for the blowoff limits of flames are shown to give excellent agreement with those concepts provided that proper account is taken of two dilution effects: composition dilution caused by entrainment and velocity gradient dilution caused by flow expansion. Approximate flow-field solutions are also derived for the unburned gas motion above an upward propagating, spherical flame kernel in buoyancy- induced flows. It is shown that the upward hemisphere propagates toward a stagnation plane in a counterflow configuration involving the balance between the combustion force, which accelerates the cold gas upward, and the buoyancy force that accelerates the cold gas downward. The position of the stagnation plane above the upward propagating hemisphere is related to the ratio of the buoyant velocity, VB, to the burning velocity, su.