The previous work of Thomas (1956) on the turbulent convection over a single, heated, horizontal surface has been extended using improved methods of analysis of the temperature fluctuations, and it has been possible to measure the distributions of mean temperature, the mean squares of the temperature fluctuation, the temperature gradient and the rate-of-change of temperature, and the statistical distributions of these quantities. These measurements were made for three different values of the convective heat flux, and the results are consistent with the dimensional consequences of assuming that the convection near the surface is independent of the distant boundaries and determined by the heat flux and the viscosity and conductivity of the fluid.

The most striking feature of the observations is that the fluctuations of temperature, temperature gradient, and rate-of-change of temperature, all show periods of activity, characterized by large fluctuations, alternating with periods of quiescence with comparatively small ones. Both the proportion and frequency of occurrence of the active periods decrease with increasing distance from the surface and they probably occur when rising columns of hot air pass through the point of observation. The quiescent periods occur when the point of observation lies outside the columns, and analysis of the statistical distributions of the various fluctuations shows that, during these periods, they are nearly independent of height. It is concluded that the quiescent fluctuations are typical of the turbulent convection far from the surface while the active fluctuations are the manifesta- tion of the convective processes arising near the rigid boundary. These processes may be described as the detachment of columns of hot air from the edge of the conduction layer and the erosion of these rising columns by contact with the surrounding air which is in vigorous turbulent motion. Since the variations of the intensities with height is dominated by the contributions of the active periods, it is not surprising that no agreement is found with the predictions of the similarity theory which assumes the convection to be independent of the conduction layer at a sufficient distance from it. The Malkus theory of turbulence, which empha- sizes dependence on the conduction layer, is in qualitative agreement with this inferred mechanism of the convection and is in quantitative agreement with the observed distribution of mean temperature. A brief discussion is given of the effect of a horizontal shearing motion on the convection and of the relation of these measurements to measurements of the temperature distribution in the earth's boundary layer with upward flux of total heat.