EHYTHMS IN DENUDATION 



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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 cycle. 



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 steep slope per unit of surface area is proportionately 

 greater. 



This argument is strictly true for the parallel walls of a valley. For 

 the circumference of a basin, however, there is really a larger volume of 

 rock between the upper contours. For hills situated within the drainage 



