## Abstract

Temperatures were measured at 200 ft. depth intervals in four boreholes in the Southern Karroo, to maximum depths ranging from 984 to 5775 ft. Some 270 conductivity measurements were made upon specimens from the cores taken from these holes, in view of the irregular variations characteristic of the sedimentary rocks penetrated. Various sources of error in the conductivity measurements are discussed, and methods are suggested for minimizing their effects. Heat flow was investigated in relation to depth, and was found to increase with depth in the three holes which were deep enough to show the effect. Large irregular variations, possibly caused by movement of ground water, increased the meansquare errors of the regression coefficients of heat flow on depth and it could not be established that the regressions were all significant. However, all regression coefficients were positive, and it became necessary to consider possible causes of variation of heat flow with depth, before equilibrium values of heat flow could be put forward. There is no reason to believe that the known geological structures would cause this effect, and it is shown that the effects of topography, and of uplift and erosion on upper limit estimates, are small compared with the observed variations. Reduction of air temperature during the ice ages of the last million years produces an effect of the right sign and magnitude. The heat-flow values in the deeper parts of the two deepest boreholes were corrected on four hypotheses with regard to Pleistocene surface temperatures. In view of the poor precision of the data it proved impossible to discriminate between these hypotheses. Correspondingly, the heat-flow values below about 2000 ft. are rather insensitive to quite large changes in assumed past climatic changes. With reasonable assumptions regarding climatic changes, no significant variation of heat flow with depth remains, and equilibrium heat flows are estimated. On climatic hypothesis D (cf. table 5) the equilibrium heat flows are: \begin{align*}&\text{Sambokkraal}&1\cdot 44 \pm 0\cdot 02 \mu cal cm^{-2} s^{-1}&\text{Koegelfontein}&1\cdot 57 \pm 0\cdot 09&\text{Bothadale}& 1\cdot 34 \pm 0\cdot 02&\text{Kalkkop}&1\cdot 31 \pm 0\cdot 07\end{align*} Heat-flow values determined in South Africa by others are included in a final discussion.