The melting curves of helium and other low boiling-point substances as determined in the laboratory might be expected to imitate those of other substances at much higher, and un-attainable, pressures. This was suggested by Simon, who with Ruhemann and Edwards later determined the melting curves of several low boiling-point substances up to about 5000 atm. pressure. There was no suggestion of any solid-fluid critical point, although the temperature reached in the case of helium was eight times the liquid-vapour critical temperature. In spite of anomalous behaviour at lower temperatures, helium is the most suitable model substance for this study, and the melting curve of helium has now been followed still further, up to about 50 degrees K and 7500 atm., with no suggestion of a critical point. Several improvements in technique have been introduced in the present investigation; the results obtained are in complete agreement with the semi-empirical formula originally proposed by Simon, Ruhemann & Edwards.