AE CONVEXIDY OF) Miri @rs: 
G. K. GILBERT 
In a maturely developed topography, hilltops composed of uncon- 
solidated 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 ago” seems to 
have been generally accepted. Its fundamental principles are (1) 
that the transporting power of a stream per unit of volume increases 
with the volume, (2) 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. 
In 1892, Davis proposed an explanation of the convexity of 
hilltops, ascribing it to creep.’ His article occupied less than a page 
of Science, and may not have attracted the attention it merited. At 
any rate Fenneman, in a recent discussion of the same subject, makes 
no mention either of Davis or of creep; and it occurs to me that a 
restatement of Davis’ explanation may be timely. 
Fenneman ascribes the convex profile to running water, making a 
distinction between the behavior of water near hilltops and lower 
down. As I find it difficult to do justice to his analysis in an abstract, 
I refrain from a comparison of his hypothesis with that of Davis, 
but refer the reader, instead, to his article which is in the Journal 
of Geology for November-December, 1908.4 
The subjoined presentation of the creep hypothesis, while essen- 
tially equivalent to Davis’, is independent in respect to various details. 
A layer of unconsolidated material resting on a gentle slope holds 
its position (1) because the particles are arranged so as-to support one 
« Published by permission of the Director of the U. S. Geological Survey. 
2 Geology of the Henry Mountains, p. 116. 
3 W. M. Davis, ‘‘The Convex Profile of Bad-Land Divides,’’ Science, XX, 245. 
4N. M. Fenneman, ‘‘Some Features of Erosion by Unconcentrated Wash,” 
Journal of Geology, XVI, 746-54. 
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