The characteristics of large, subglacially formed eskers, such as the Katahdin system, are closely related to two special peculiarities of water-filled tunnels along the beds of ice sheets: (1) the water pressure approximates the weight of the overlying ice; and (2) in tunnels that descend and those that ascend less steeply than ∼1.7 times the ice-surface gradient, the walls melt, producing a sharply arched tunnel cross section, whereas in those that ascend more steeply, they freeze, producing a wide, low one. The first peculiarity primarily governs the paths of these eskers. It causes the tunnels to follow the paths ordinary rivers would follow were the land tipped downglacier ∼11 times the local ice-surface gradient. The paths therefore trend in the general direction of the former ice flow but tend to deviate so as to follow valleys and to cross divides at the lowest passes, as observed. Ice-surface gradients calculated from path deviations at two localities on the Katahdin esker system indicate relatively thin, sluggish ice the surface of which lay ∼200 m below the summit of Mount Katahdin, in agreement with independent geologic evidence. The second peculiarity primarily governs the form, composition, and structure of these eskers. Strong melting causes a large inflow of basal ice and entrained debris to the tunnel and produces sharp-crested eskers of poorly sorted, poorly bedded sand, gravel, and boulders with lithologies like the adjacent till, whereas weaker melting produces multiple-crested ones of similar composition. Freezing precludes inflow and produces broad-crested eskers of fairly well-sorted, well-bedded, more water-worn, coarse sand with few large clasts. Ice-surface gradients calculated from transitions from the multiple-crested type to small areas of broad-crested type on the Katahdin system agree closely with those computed from the paths at nearby localities. An anomalously low gradient calculated from a transition to an area of broad-crested type approximately twice as wide and long as the probable ice depth apparently confirms that, as expected, the basal ice was supported by water pressure over most, if not all, of the width of the esker.