The Convexity of Hilltops

In a maturely developed topography, hilltops composed of unconsolidated materials are upwardly convex in profile. Their forms are thus contrasted with the longitudinal profiles of stream beds, which in mature development are concave upward. An explanation of the river profile offered by the writer more than thirty years ago2 seems to have been generally accepted. Its fundamental principles are (i) that the transporting power of a stream per unit of volume increases with the volume, (z) that transporting power increases with the slope, and 3) that a stream automatically adjusts slope to volume in such way as to equalize its work of transportation in different parts.