  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.

Fluid Dynamics