7t)8 J. BARRELL^MEASUEExMEXTS OF GEOLOGIC TIME 



basin, on the other hand, there is a lesser volume. This and the lesFe^ 

 erosive power of the rain not vet gathered into rills gives such liills a 

 convex profile across the top as the profile of equilibrium. 



It is seen furthei' that the main river, with its greater volume of water, 

 comes to How on a tlatter slope than its tributary, and thus there is au 

 adjustment in equilibrium. The erosion of a soft formation on a flatter 

 slope is in adjustment also with the associated hard formation Avith a 

 much steeper slope. 



Another line of evidence on the large influence of angle of slope is seen 

 in the geological speed with which the early stages of a new erosion cycle 

 are completed. On a new pulse of uplift the river becomes entrenched 

 near its mouth and this entrenchment migrates toward the head waters. 

 It advances far up the stream and changes from youth to maturity, while 

 the older part of the valley has changed its character but little. Eiver 

 piracy is another result of the same effect. If a river obtains an advan- 

 tage in depth it will cut into the basins of other rivers rising from the 

 same watershed. The steeper slopes enable it to remove much more ma- 

 terial in the same time interval, and this is a necessary condition for river 

 pirac}', although after the capture is effected the added water then gives 

 the river still greater corrasive power. 



The pluvial, or stream profile, and the fiuvial, or cross-profile, of a 

 valley must show different relations of rate of erosion to angle of slope. 

 The stream profile is not only cut much faster, hut is long and flat and in 

 equilibrium with a valley cross-section of far higher slope. The result is 

 seen in the rapid cutting of gorges as the initial effect of uplift, followed 

 by the far slower w^eathering back of these, accompanied by only a slight 

 further flattening of the stream profile. Flowing water has Ijeen theo- 

 retically argued to erode as the square of its velocity, and its moving force 

 to increase with the sixth power of the velocity. Gilbert found from ex- 

 perimental work that 



"for each combination of discharge, width, and grade of debris there is a slope, 

 called competent slope, which limits transportation. With lower slopes there 

 is no load, or the stream has no capacity for load. With higher slopes capacity 

 exists ; and increase of slope gives increase of capacity. The value of capacity 

 ivS approximately proportional to a power of the excess of slope above compe- 

 tent slope. If *S' equal the stream's slope and 5 equal competent slope, then 

 the stream's capacity varies as (8-8) n. This is not a deductive, but an em- 

 piric law. The exponent n has not a fixed value, but an indefinite series of 

 values depending on conditions. Its range of values in the experience of the 

 laboratory is from 0.93 to 2..37, the values being greater as the discharges are 

 smaller or the debris is coarser." ^'' 



^ G. K. Gilbert: The transportation of debris by ruiininji Avater. Prof. Paper 86, U- S. 

 Geol. Survey, 1914, p. 10. 



