The electron swarm parameters in Hg/Ar and Hg/Ar/0.1%H₂ mixtures are analyzed using a Boltzmann equation in which the generation of secondary electrons through Penning and cumulative ionization, and collisions between two metastable Hg (Hg^*) atoms are taken properly into consideration. The present values of the Townsend first ionization coefficient and the concentration of Hg^* agree well with the experimental values of Burgumann et al. and Bigio respectively. It is shown that mixing 0.1%H₂ in Hg/Ar lowers the ionization coefficient significantly. This lowering effect is discussed how it influences the characteristics of discharge lamps.