Gilbert's exception to law of divides. 139 



divides, as stated in a previous paragraph, the profile of any slope in the bad-lands 

 should be concave upward, and the slope should be steepest at the divide. The 

 union or intersection of two slopes on a divide should produce an angle [figure 6]. 

 But in point of fact the slopes do not unite in an angle. They unite in a curve, and 

 the profile of a drainage slope, instead of being concave all the way to its summit, 

 changes its curvature and becomes convex. . . . From a to m [figure 7] and 

 from b to n the slopes are concave, but from m to n there is a convex curvature. 

 Where the flanking slopes are as steep as represented in the diagram, the con- 

 vexity on the crest of a ridge has a breadth of only two or three yards, but where 

 the flanking slopes are gentle, its breadth is several times as great. [Compare 

 figure 5 with figure 7.] It is never absent. 



Fku'kk 7. *— Cross-profile of bad-land' Divide. 



" Thus in the sculpture of the bad-lands there is revealed an exception to the 

 law of divides, — an exception which cannot be referred to accidents of structure, 

 and which is as persistent in its recurrence as are the features which conform to 

 the law, — an exception which in some unexplained way is part of the law. Our 

 analysis of the agencies and conditions of erosion, on the one hand, lias led to the 

 conclusion that (where structure does not prevent) the declivities of a continuous 

 drainage slope increase as the quantities of water flowing over them decrease, and 

 that they are great in proportion as they are near divides. Our observation, on 

 the other hand, shows that the declivities increase as the quantities of water 

 diminish, up to a certain point where the quantity is very small, and then de- 

 crease; and that declivities are great in proportion as they ai'e near divides, unless 

 they are very near divides. Evidently some factor has been overlooked in the 

 analysis, — a factor which in the main is less important than the flow of water, but 

 which asserts its existence at those points where the flow of water is exceedingly 

 small, and is there supreme." 



The missing factor is a simple and omnipresent one, namely, weather- 

 ing. From a to m the water curve predominates, and its law of skyward 

 concavity and increasing declivity is supreme. From m to h the weather 

 curve predominates. As Gilbert remarks, "the flow of water is exceed- 

 ingly small" there. It falls as rain and beats upon the crest, hut that is 

 a kind of weathering. 



Besides supplying the missing factor which explains the puzzle and 

 reconciles the results of scientific analysis with the facts as learned by 



* Figure 7 is a reproduction of Gilbert's figure 60, in his Report on the Geology of the Henry 

 Mountains, p. 123. 



