. Bulletin of the Geological Society of America. Geology. EHYTHMS IN DENUDATION 75^ ffliicli depends on it, especially as the writer has recently heard it stated by an able geologist that in his opinion the angle of slope had but little influence; the rate, on account of various compensating factors, continu- ing, in his opinion, high until old age was attained. This geologist pointed out as evidence that lowdand streams may he silt-laden and show^ a high rate of denudation, whereas mountain streams are clear. Without denying these facts, the wTiter would give them a widely different inter- pr
. Bulletin of the Geological Society of America. Geology. EHYTHMS IN DENUDATION 75^ ffliicli depends on it, especially as the writer has recently heard it stated by an able geologist that in his opinion the angle of slope had but little influence; the rate, on account of various compensating factors, continu- ing, in his opinion, high until old age was attained. This geologist pointed out as evidence that lowdand streams may he silt-laden and show^ a high rate of denudation, whereas mountain streams are clear. Without denying these facts, the wTiter would give them a widely different inter- pretation and holds that denudation in the same roch formation varies with the slope, and probably at a somewhat higher rate than the change in the angle of slope. The problem is complicated and the relationship must vary w4th climate and rock formation. It is not as yet susceptible of pi'ecise statement. To the writer it appears probable, however, that the rate of pluvial and fluvial denudation in the same formation and under constant rainfall varies between the first and second power of the angle of slope. A strong argument that the rate of denudation varies with slope is de- rived from the nature of the profile of a graded stream and of the cross- section of a mature valley as developed in a single erosion Figure 1.—Stages in a graded Valley Profile cut in a homogeneous Formation A valley profile, if a graded slope in a homogeneous rock, is a curved slope, as shown in figure 1. Let A E and A' E' be two successive stages in the erosion of the valle}^, stages sufficiently close so that the character of the curve does not change in the interval. Then A A' = B B' = EE'. Let equal contour intervals A B, B C, etcetera, be taken and the A^olumes of rock, A A'-B B', removed between each contour interval are equal. But the erosion surface A B for the unit volume of erosion on the steep slope is very much less than for D E on a flat slope. Therefore the rate of erosion on the
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