The theory of Nye and of Weertman of traveling waves on glaciers is extended to cover the situation where the presence of abundant basal water or increased basal water pressure produces increased sliding of a glacier over its bed. It is found that the ratio of traveling-wave velocity to surface velocity is independent of the amount of water or the basal water pressure. The theoretical value of this ratio, about 4 to 5, agrees with that found in field measurements (the most recent data are from

more »

... er de Glace). It is concluded that field observations of traveling-wave velocities lend strong support to any glacier sliding theory in which the sliding velocity is proportional to the basal shear stress raised to about a second to fifth power and in which the sliding velocity is a function of either or both the amount of water at the bed of a glacier and the pressure within this water.