The measurement of the intensity of fluorescence of metals in the vapour phase as a function of the partial pressure of other gases is the usual method used to determine the quenching cross-sections of metals by other atoms and by molecules. For atoms with two close-lying upper levels, such as the alkali metal atoms, the values deduced for the quenching cross-sections by the Stern-Volmer plot may not be equal to the cross-section for any specific process but only effective values which are functions of the actual ones. In this paper the relationships between the intensity of fluorescence, the pressure of foreign gas and the actual quenching rates are derived and the experiments which would enable the true values to be deduced are identified.