The concept of limit burning velocities, formulated in an earlier Bureau of Mines report (ri 8127) is applied to the problem of flame propagation through tubes of finite size. The limit burning velocity for conductive-convective wall-loss quenching (process b) is (su)b = ape/2ro, where the proper choice of critical peclet constant, pe, is determined mainly by the ratio of contact-perimeter loss area to flame-zone cross-sectional area. This ratio of loss area to propagation area relates to the shape of the flame front and its control by buoyancy and by boundary conditions. The comparison of (su)b with previously defined limit velocities for systems mixed by natural convection allows one to assess the influence of tube dimensions and boundary constraints on the "true" or earthly limits for the three directions of propagation. The flame quenching caused by inert powders is shown to be similarly described in terms of a limit burning velocity, (su)'b. The tube's surface-to-volume ratio ( 1/ro) is simply replaced by the powder's surface area per unit volume of the flammable mixture. Thermal loss quenching by these "internal walls" occurs at a critical peclet constant somewhat higher than that observed for tubes, and the problem is complicated by the finite heat capacities of the powders and particle lag effects in the flame front.