  Measurements of the Nusselt number $Nu$ and of temperature variations $\Delta
T_b$ in the bulk fluid are reported for turbulent Rayleigh-B\'enard convection
of a cylindrical sample. They cover the Rayleigh-number range $10^{9} \alt Ra
\alt 3\times 10^{14}$ using He (Prandtl number $Pr = 0.67$), N$_2$ ($Pr =
0.72$) and SF$_6$ ($Pr = 0.79$ to 0.84) at pressures up to 15 bars and
near-ambient temperatures. The sample had a height $L=2.24$m and diameter $D =
1.12$m and was located in a new High-Pressure Convection Facility (HPCF) at the
Max Planck Institute for Dynamics and Self-Organization in G\"ottingen,
Germany. The data do not show the transition to an "ultimate regime" reported
by Chavanne et al. and are consistent with the measurements of Niemela et al.
