. Bulletin of the Geological Society of America. Geology; Geology -- United States. 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
. Bulletin of the Geological Society of America. Geology; Geology -- United States. 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 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 overl
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