At a time when nobody has yet landed on the Antarctic continent (1879), this presentation and accompanying paper predicts the morphology, dynamics and thermal regime of the Antarctic ice sheet. Mathematical modelling of the ice sheet is based on the assumptions that the thickness of tabular icebergs reflects the average thickness of the ice at the margin and that the surface gradients are comparable to those of reconstructed former ice sheets in the Northern Hemisphere. The modelling shows that (a) ice is thickest near the centre at the South Pole and thins towards the margin; (b) the thickness at the pole is independent of the amount of snowfall at that place; and (c) the mean velocity at the margin, assuming a mean annual snowfall of two inches per year, is 400–500 feet per year. The thermal regime of the ice sheet is influenced by three heat sources – namely, the bed, the internal friction of ice flow and the atmosphere. The latter is the most significant and, since ice has a downwards as well as horizontal motion, this carries cold ice down into the ice sheet. Since the temperature at which ice melts is lowered by pressure at a rate of 0.0137 °F for every atmosphere of pressure (something known since 1784), much of the ice sheet and its base must be below the freezing point. Estimates of the thickness of ice at the centre depend closely on the surface gradients assumed and range between 3 and 24 miles. Such uncertainty is of concern since both the volume and gravitational attraction of the ice mass have an effect on global sea level. In order to improve our estimate of the volume of ice, we will have to wait 76 years for John Glen to develop a realistic flow law for ice.