BELATION OF CAPACITY TO DISCHARGE. 



139 



The same data are plotted in figure 47, where 

 horizontal distances represent logarithms of dis- 

 charge and vertical distances logarithms of ca- 

 pacity. For each of the above-mentioned 

 " groups " the plotted points are connected by a 

 series of straight lines, and each of the broken 



FIGURE 47. Logarithmic plots of the relation of capacity to discharge. 

 The horizontal scale is that of log Q, the vertical of log C. The zeros 

 of log C for the different plots are not the same. 



lines thus produced is the rough logarithmic 

 graph of an equation C=*f(Q). The graphs 

 are arranged according to grades of debris, and 

 secondarily according to widths of channel, 

 their order from left to right corresponding to 

 the sequence from narrower to broader channels. 

 In effecting this arrangement graphs were 



moved bodily up or down but not to the right or 

 left. 



It appears by inspection that the graphs 

 bend toward the right as they ascend. To this 

 rule there are a few exceptions, but the only 

 strongly marked exceptions are connected with 

 grade (E), the data for which have previously 

 been recognized as anomalous. As the incli- 

 nation of each line indicates the sensitiveness of 

 capacity to the control of discharge, the general 

 bending to the right, or the reduction of inclina- 

 tion in passing from lower to higher discharges 

 shows that sensitiveness diminishes as dis- 

 charge increases. This feature is similar to one 

 observed in studying the relation of capacity to 

 slope, and as that feature was found to be con- 

 nected with competence, the resemblance leads 

 at once to the suggestion that here also is a con- 

 nection with competence. 



If a very small discharge be made to flow 

 over a sloping bed of debris and the discharge 

 be gradually increased, transportation of ddbris 

 wiU commence when the competent discharge 

 is reached and will increase with further in- 

 crease of discharge. It is a plausible hypothe- 

 sis that the capacity is more simply related 

 to the excess of discharge above the competent 

 quantity than to the total discharge. Follow- 

 ing the procedure in the case of capacity and 

 slope we may assume that capacity is propor- 

 tional to a power of the excess of discharge 

 above a constant discharge, the constant dis- 

 charge being closely related to competent dis- 

 charge. In the following formula, constructed 

 on the plan of equation (10), 



C=1 3 (Q-K} ...(64) 



K is a constant discharge and & 3 is a constant 

 numerically equal to the value of capacity 

 when the discharge equals x+1, although it is 

 not strictly a capacity. The dimensions of 

 capacity are M +l T' 1 , of discharge L +3 T' 1 , and 

 of (Q-K) L +3 T-; and these values give to 

 6 3 the dimensions L' 30 M +l T~ l . 



As a preliminary to the adjustment of the 

 observational data of Table 32 by this formula, 

 values of were graphically computed by the 

 method previously employed in connection 

 with a. The computations were applied to all 

 groups of values of capacity in the table, 

 except such as comprise less than three capaci- 

 ties and except also the aberrant data of grade 

 (E). In Table 33 the results are arranged 



