The total cross sections for the scattering of positrons by helium have been measured by the method of transmission in the 16 to 270 eV energy range. The experimental results are higher than those of Canter et al. but are in reasonable agreement with recent results of Griffith et al., and at high energies tend towards Born approximation calculations. The integral of the cross section over positron momentum is smaller than the sum rule estimate made by Bransden et al. A tentative value of (0.034 ± 0.017)πa02 is assigned to the positronium formation cross section at threshold.