The formation of positronium in gases can be investigated by observing the energy spectrum of the annihilation radiation. The increase in positronium formation due to a static electric field has been measured in various gases. For the rare gases the increase has a sigmoid dependence on the ratio of electric field to pressure. The fraction of the positrons that form positronium increases by a maximum factor of 1.5, 1.4, and 2.1 for He, Ne, and A, respectively. A similar increase was observed for H2, D2, and N2. No effect of the electric field was found in the polyatomic gases CO2, CH4, C2H6, and CCl2F2, but a small anomalous decrease in positronium formation was seen in SF6. The increase in positronium formation occurs in the presence of an electric field because low energy positrons, which die by direct annihilation with atomic electrons without positronium formation in the absence of an electric field, can gain energy from the electric field to cross the threshold energy for positronium formation in the gas. A theory based on the Boltzmann equation describes the behavior of the positrons under the combined influence of the electric field and molecular collisions, and provides the basis for obtaining from the observed data values of the elastic scattering cross section of positrons by the rare gas atoms. The cross sections are 0.023πa02, 0.12πa02, and 1.5πa02±25% for He, Ne, and A, respectively. Quantitative interpretation for the polyatomic gases is more difficult. An optical search for the 2430 A Lyman line from positronium is described.