An observational study of cumulus is made from time-lapse film records, and laws describing the growth of cloud thermals (discrete masses of buoyant air) are deduced. The diameter of isolated thermals emerging from the summits or on the flanks of a cumulus is found to have a well-defined upper limit which is a simple linear function of height. It is inferred that, in the saturated interior of a cloud, thermals broaden linearly with height incorporating into themselves the residues of earlier (now decaying) thermals. Their rate of broadening with height, 0.40 ± .04, is found insensitive to variations of the stability and humidity of the cloud layer and to the presence or absence of precipitation. From the observed broadening, the buoyancy of cloud thermals can be deduced if a knowledge of the properties of decaying thermal residues is given. A probable upper limit to thermal buoyancy is computed and is found to be some fraction of the adiabatic value. Observations of the rate of rise and the diameter of the most vigorous thermals emerging from the cloud interior and estimates of their buoyancy permit a test of a proposed simple relationship between these properties. Fair agreement is obtained in the statically unstable part of the cloud layer. Thermals with smaller rates of rise are deduced to have smaller buoyancy due to their growth in less favorable environment. The relation between the properties of cloud thermals and the history of the cloud is indicated. Both the quantitative and qualitative results of the investigation establish the ‘thermal theory’ of cumulus convection on a firmer basis than hitherto.