Resonance emission at λ 1849 Å was measured at right angles to a λ 1849 Å source as a function of quenching gas pressure in a system containing Hg vapor at room temperature. The emission intensity varied with pressure in accordance with the Stern-Volmer relationship. Cross sections for the quenching of Hg(1P1) relative to N2 were calculated from the relative slopes of the Stern-Volmer plots for 12 gases (including Ne and Ar) with molecular weights ranging from 2 to 200. The relative quenching cross sections fell in the range 0.2-3.0 and generally increased with increasing molecular weight. Quenching by He was not detectable. The relatively small differences in these values stand in contrast to the much larger differences in quenching cross sections for Hg(3P1). A number of relative quenching cross sections at λ 2537 Å were measured in the same apparatus and agreed with literature values.