Experiments in which a thick layer of fluid was heated from below at a constant rate were conducted at flux Rayleigh numbers in the range of 109to 1012. The resulting convection was investigated by statistical analysis of the temperature signals from a pair of thermistor probes at different horizontal spacings. Power spectra showed that the temperature variance was distributed over a broad band of periods but that the centroid of this band, the characteristic period, depended very nearly on the − (1)/(2) power of the heat flux. Measurements of the coherency between the probe signals at varying distances were interpreted as defining a characteristic horizontal length scale that depended approximately upon the − (1)/(4) power of the heat flux. These results tend to substantiate the boundary layer instability model of convection at very high Rayleigh numbers.