The HARP system of resistive plate chambers (RPCs) was designed to perform particle identification by the measurement of the difference in the time-of-flight of different particles. In previous papers an apparent discrepancy was shown between the response of the RPCs to minimum ionizing pions and heavily ionizing protons. Using the kinematics of elastic scattering off a hydrogen target a controlled beam of low momentum recoil protons was directed onto the RPC chambers. With this method the trajectory and momentum, and hence the time-of-flight of the protons can be precisely predicted without need for a measurement of momentum of the protons. It is demonstrated that the measurement of the time-of-arrival of particles by the thin gas-gap glass RPC system of the HARP experiment depends on the primary ionization deposited by the particle in the detector.