The theory of fuel-reservoir fires (that is, pool flames) is extended and amplified into a quantitative formulation that includes all the significant physical processes--mass diffusion, heat conduction, convective mixing, convective heat transport, and radiative heat transport. The conservation equations across the gibbsian surfaces of the pool flame are solved, in finite-difference form, under idealized but nevertheless realistic conditions. This semiempirical solution, which quantifies the consensus of views of many previous researchers, is surprisingly simple considering the number of processes involved and their complexity. The predictions are compared with the data for three fuels (gasoline, liquid hydrogen, and methanol), and the comparison gives reasonable agreement. This steady-state theory idealizes the complexities of turbulent, eddy mixing in terms of a single, average mixing radius, whose magnitude is inferred from the observed flame structures. The radiative transport process from the hot flame volume to the pool reservoir is idealized as a planar surface-to-surface transfer function. The observed flame thickness is used to calculate both the emissivity of the upper "flame surface" and its average height above the pool. The theory presented is only a beginning in handling the major problem, that is, the feedback loop between the combustion source function and the flow mixing of vaporizing fuel with entrained air. Combustion and buoyancy forces are the sources of flow, but it is the flow mixing field itself that controls the strength of these forces.