  The mean-square displacement (MSD) was measured by neutron scattering at
various temperatures and pressures for a number of molecular glass-forming
liquids. The MSD is invariant along the glass-transition line at the pressure
studied, thus establishing an ``intrinsic'' Lindemann criterion for any given
liquid. A one-to-one connection between the MSD's temperature dependence and
the liquid's fragility is found when the MSD is evaluated on a time scale of
approximately 4 nanoseconds, but does not hold when the MSD is evaluated at
shorter times. The findings are discussed in terms of the elastic model and the
role of relaxations, and the correlations between slow and fast dynamics are
addressed.
