The carrier phase at 40 MHz on the ATS 6 to Boulder beacon experiment is found to be sufficiently well resolved to allow the measurement of the second-order term as well as the first-order total electron content value. The second-order component of phase path is primarily due to a truncation of the expansion for refractive index when the satellite is within about 45° of zenith, but it is dominated by ray path bending when the satellite is outside that zone. The second-order value is used to derive scale height at the peak of the F layer for one day of data with absolute accuracy of about ±10% during the daytime, when the plasma densities are generally high. The scale height determined at the peak differs from that derived from ionograms for the underside of the peak and also differs from that of the α-Chapman layer fitted to total content and peak density. The main advantage of the second-order evaluation of scale height is its spatial coincidence with total content and F factor observations.