126 



TBANSPOBTATION OF DEBEIS BY BUNNING WATEB. 



Substituting for d its equivalent 

 Cxw(l-aR). 



d 



As d is by postulate constant, and as w = -^ 



H 



w oc-g. We may therefore substitute -= for w in 

 K ti 



the proportion above, obtaining 

 1-aR 



Cx- 



R 



-(49) 



This expression gives the relation of capacity 

 to form ratio, so far as that relation depends 

 on variation of width. Eventually it is to be 

 complemented by an expression similarly 

 dependent on variation of depth. 



The preceding analysis involves the assump- 

 tion that the stream is so broad, in relation to 

 its depth, that its medial portion is unaffected 

 by lateral influences. The resulting proportion, 

 (49), is not necessarily applicable to narrower 

 streams. It is quite conceivable that when 

 the channel is so narrow that the reaction of 

 the sides affects all parts of the current the 

 variation of capacity follows a different law. 

 The analytic consideration of the case of 

 narrower channels has not been attempted, 

 but some information has been obtained from 

 the experiments. The following examination 

 of experimental data is directed toward this 

 question and also toward that of the magnitude 

 of the constant a. 



TABLE 24. Relation of capacity for traction to width of channel, when slope and depth are constant. 



The assumptions of the present section 

 include constant slope and constant depth, 

 with discharge and capacity adjusted to varia- 

 tion of width. The experiments involve con- 

 stant width and constant discharge, with 

 automatic adjustment of slope and depth to 

 variation of load. In order to check the 

 analysis by means of the laboratory data it is 

 necessary to employ some method of inter- 

 polation. Two methods were tried, but only 

 one need be described. 



Attention being first restricted to a par- 

 ticular grade of d6bris and a particular slope 

 of channel, the computation sheets (p. 95) 

 for the different discharges were entered with 

 a particular depth as argument, and the 

 associated values of capacity and slope were 



taken out. These values were plotted on 

 logarithmic section paper as a series of points. 

 Through these points was drawn a curve the 

 locus of log (7=/(logS), under the condition 

 that d is constant. By means of this curve 

 values of C were interpolated, corresponding to 

 selected values of S. The process was then 

 repeated with other depths, other widths, and 

 other grades ; and in this way were obtained 

 sets of values of capacity in relation to width, 

 under the condition of constant depth and 

 slope. Such interpolated values of capacity 

 are presented in Table 24. It was found that 

 the data for grades (B) and (C) only are full 

 enough to serve the present purpose. 



The tabulated capacities are also plotted, in 

 relation to width, in the upper and second divi- 



