A thorough investigation of Lewis' formal solution of the multiple scattering problem for an infinite medium is presented. The account includes the mean value and the longitudinal dispersion of the projected range distribution and also the transverse dispersion for 10-3000 keV electrons and positrons in a number of monatomic targets. A method for comparison with experimental data is described and applied. Approximate results for semi-infinite targets are shown to compare well with experiments even for heavy elements where the deviations relative to infinite targets are shown to be most pronounced and related to the probability of back-scattering. Finally, the authors note that an unresolved discrepancy appears to persist between theoretically and experimentally determined differences of electron and positron penetration.