An apparatus for the measurement of positron and electron total cross sections on gases is described. The low-energy positrons are produced by moderating high-energy positrons from beta -decay sources. The authors used a 11C positron source, produced at a proton accelerator and, alternatively, a 22Na source, combined with various moderators. For electron measurements the secondary electrons originating from the moderator are used. The beam transport system consists of electrostatic lenses and a weak magnetic lens located in the middle of the gas cell. The discrimination against forward scattering is characterised by a cut-off angle of about 6 degrees . The authors' e+-H2 and e--H2 data are compared with the results of recent measurements of similar accuracy performed at University College, London, and Wayne State University (Detroit), and with other e--H2 data. The agreement is satisfactory.