In a combustion context (there are other possible applications), the problem considered is of a strong air jet issuing normal to a furnace wall (the burner wall) and a weak fuel jet (typically of natural gas) issuing at an angle some distance away. The atmosphere surrounding the jets is of slow-moving there taken as stagnant) combustion products, as is normal in a furnace. The jet port axes are coplanar and divergent. The fuel jet is weak because of normal combustion stoichiometry which dictates that the air flow be much greater than that of the fuel. Simple jet physics is applied to the problem. The fuel jet describes a curving trajectory and is eventually entrained by the air jet. The trajectories of both jets are predicted, as is the entrainment of ambient fluid, up to the region of confluence. The trajectories agree well with experimental measurements. The two-jet mixing zone which follows the meeting of the jets and the succeeding final dilution zone which is dominated by continuing dilution with entrained furnace gases are described. The work provides a foundation for the analysis of a new class of burners that inject fuel and air directly into the furnace chamber (not into a burner quarl, tile, or "combustion tunnel"), so both fuel and air mix, by natural furnace aerodynamics, with substantial quantities of furnace gases, partly cooled by furnace heat transfer, before they meet and react. This results in remarkably low NOx emissions.