AVERAGE REGIONAL SLOPE 41 



If, for instance, the slope, expressed in percentage of fall to hori- 

 zontal distance, was doubled, the load dragged was, in the experi- 

 ments, increased three to more than tenfold. Conversely as the 

 slope decreased, the load decreased, but at a greater rate. 



The load carried in suspension is partly a function of the stream's 

 velocity, and depends partly upon the fineness and amount of 

 debris supplied. In experiments made on streams without load, 

 the velocity was found to vary approximately as the 0.3 power of 

 the slope, and the 0.25 power of the discharge. 1 



The size of pebbles which can be carried in suspension varies as 

 the fifth power of the velocity; that is, if velocity were unaffected 

 by the addition of debris, it would vary approximately as the ■§■ 

 power of the slope. Velocity is diminished by suspended matter, 

 but not enough to make the factor of f less than unity. It is prob- 

 able that in the majority of cases the grading of debris supplied 

 to a stream is such that, if the slope be increased, the maximum load 

 of suspended material carried by a stream will increase at a rate 

 comparable to the rate of increase of the size of debris carried; 

 that is, it will increase at a slightly greater rate than the increase 

 in slope. Conversely if the slope be decreased, the maximum load 

 carried in suspension will be decreased but at a greater rate than 

 the slopes. 



If discharge and fineness of debris supplied remain the same, 

 therefore, both the maximum load dragged along a stream bed and 

 that carried in suspension decrease at a greater rate than the slope, 

 and the difference in the rate of decrease of the two functions 

 becomes greater as the slopes decrease. This law of variation is 

 applicable to natural streams as well as to those in the laboratory. 2 



But changes in discharge and fineness of debris as old age pro- 

 gresses, both tend to reduce further the load carried. For the rain- 

 fall on a land form, the size of a geographic unit is likely to decrease 

 as the land becomes lower, and the proportion of runoff to rainfall 

 will also decrease so that the discharge of the streams would 

 decrease. The debris supplied to the streams, moreover, becomes 



1 Ibid., 225. Discharge is defined as the number of cubic feet of water passing 

 a given point per second. 



2 Gilbert, op. cit., p. 233. 



