EROSION BY UNCONCENTRATED WASH 753 



below, and that level has no existence for the current above the fall. 

 Nor is it necessary that the fall be vertical; the principle is the same 

 in the approach to a cataract or cascade or other exceptionally steep 

 slope, though its application is less simple. 



Applying this principle to the case of rill-wash, we recall that 

 the end of the overloaded condition and the beginning of gully-cutting 

 is sudden. The effect of this is a steep offset which allows the rills 

 to cut down without reference to any lower limit. The effect of this, 

 in turn, is progressively increased slope as the fall at the gully-head 

 is approached. This gives, above the gully-head, a profile which is 

 convex upward, which gives way in the young valley itself to a profile 

 of decreasing slope, that is, one which is concave upward. It will 

 readily be seen that this description fits the case of the simple gully 

 developed on a simple slope. Indeed the compound curve thus 

 formed is very general despite all complexities due to sod covering 

 and initially complex slopes. 



A similar convexity of the upper slope is seen in the cross-section 

 of a young valley. The existence of the valley removes from the 

 wash on at least the upper part of the slope, the influence of the level 

 which limits down-cutting. In all cases, therefore, except where 

 peculiar conditions are assumed, the wash increases in power for a 

 small distance at least, while the slope is concurrently steepened, 

 producing a curve which is convex upward. If the valley be deepen- 

 ing, this convexity approaches more or less close to the axis, and, 

 if the deepening be sufficiently rapid, the convexity reaches the channel 

 making the entire slope from hilltop to stream convex upward. Where 

 this is the case, the down-cutting of the valley axis is sufficient to leave 

 the rill-wash on the entire slope free from the influence of a lower 

 limiting level. Where down-cutting is less rapid, the wash near 

 the stream comes within the influence of a lower limit and shapes 

 its profile according to the laws of streams, that is, it becomes con- 

 cave upward. The result is the U-shaped valley. The point to be 

 emphasized here is that not only does this form not imply a cessation 

 of down-cutting, but that it does not even imply lateral corrasion by 

 the stream. The only requisite is that the stream shall cut down 

 slowly enough so as not to remove from the wash on the side slopes 

 the influence of a lower limit. In the area mentioned near St. Louis 



