Absolute electron impact cross sections for single ionisation leaving H l in its electronic ground state and double ionisation leading to dissociation into all four constituents have been determined by a direct method in the energy range 0.15-2.6 keV. The values for single ionisation are in perfect agreement with, but the double-ionisation values are much larger than, the earlier determination by Edwards et al. Our results exhibit a close relationship between the H, system and its atomic counterpart, helium, with respect to their response to single-and double-ionisation processes.