The calculation of atmospheric transmission functions for infrared spectral lines having a pressure-broadened line shape is extended to include the case where the fractional concentration of the radiating gas varies with height. The radiation exchange between two atmospheric layers can now be calculated under a wide variety of conditions. A recent formulation of the radiation problem by Plass is used to show that the conversion factor for changing parallel-beam radiation to diffuse radiation varies between one and two, depending on the particular frequency interval and optical thickness considered. The value of the conversion factor is two for a frequency interval involving only very weak lines; the value is 1.78 when the centers of the lines are black, if the lines do not overlap appreciably; the value approaches unity as the lines overlap more and more. The use of an average value for the conversion factor can lead to errors of 17 per cent in the calculation of radiation exchange. Since the angular integrations necessary to obtain the diffuse radiation are often considerably easier to perform when the correct line shape is used than when its frequency dependence is neglected, there appears to be no reason to introduce an additional uncertainty in radiation calculations by the use of an average value for the conversion factor to diffuse radiation. It is also shown that the radiation exchange for a strong line can be obtained for the varying pressure conditions in the atmosphere merely by a change of variables in the result for the transmission function of a slab under constant pressure conditions.