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ICE-SHEETS, such as those of the Pleistocene epoch and those that now cover Greenland and the Antarctic continent, are in a state of quasi-static equilibrium in which the tendency of the ice to spread laterally and to flow downhill under its own weight is just balanced by the inward shear force exerted by the rock floor. By estimating the magnitude of this shear force, it is possible to make an approximate calculation of the thicknesses of the ice. We may consider first a slab of ice of large extent and of uniform thickness h resting on a plane bed of inclination ex. If the stresses are the same on every cross-section perpendicular to the line of greatest slope, resolution of forces down the slope shows that the shear stress on the bed is

,= pgh sin ex,(I) where p is the density and g is the gravitational acceleration. We now allow the thickness and slope to vary slowly from point to point. Let the surface be of slope ex in the region …