We report studies of ultrahigh-energy cosmic-ray composition via analysis of depth of air shower maximum (X(max)), for air shower events collected by the High-Resolution Fly's Eye (HiRes) observatory. The HiRes data are consistent with a constant elongation rate d<X(max)>/d[log(E)] of 47.9+/-6.0(stat)+/-3.2(syst) g/cm2/decade for energies between 1.6 and 63 EeV, and are consistent with a predominantly protonic composition of cosmic rays when interpreted via the QGSJET01 and QGSJET-II high-energy hadronic interaction models. These measurements constrain models in which the galactic-to-extragalactic transition is the cause of the energy spectrum ankle at 4x10(18) eV.