The equations of Milsom are evaluated, giving the ground range and group delay of radio waves propagated via the horizontally stratified model ionosphere proposed by Bradley and Dudeney. Expressions for the ground range which allow for the effects of the underlying E- and F1-regions are used to evaluate the basic maximum usable frequency orM-factors for single F-layer hops. An algorithm for the rapid calculation of theM-factor at a given range is developed, and shown to be accurate to within 5%. The results reveal that theM(3000)F2-factor scaled from vertical-incidence ionograms using the standard URSI procedure can be up to 7.5% in error. A simple addition to the algorithm effects a correction to ionogram values to make these accurate to 0.5%.