Studies have been made of the production of slow (∼1 eV) positrons by high‐energy positrons from a radioactive source. Moderators consisting of thin metallic foils coated with MgO smoke were used in the transmission mode. The thinnest foils gave the largest fluxes of slow positrons. A double moderator, consisting of a MgO‐coated grid following the MgO‐coated thin foil, gave a flux almost double that of either the foil or grid alone. The positron beam machine used is described. It has electrostatic optics for the collection, analysis, and transmission of the slow positrons.