EELATION OF CAPACITY TO DISCHARGE. 



149 



i 1 

 In Table 42 the values of -^ =- correspond to 



*3~ 



n 



those of . 1 ,- in Table 41 and are similarly 



\~ 

 derived from data of Tables 27 to 40. The pur- 



pose of the table is to show how the dominance 

 of control by slope, aa expressed by a ratio, 

 varies with certain conditions. 



A comparison of tabulated values for the 

 several ratios shows that the ratios associated 

 with efficiency vary with conditions more rap- 

 idly than those associated with capacity, but 

 less rapidly than those associated with duty. 

 In Table 42, just as in Table 41, there are no 

 exceptions as to the direction of the trend of 

 variation. 



Bearing in mind that the alphabetic order in 

 which the grades are arranged is the order from 

 fine to coarse, and that variation with respect 

 to form ratio is the inverse of variation with 

 respect to width, we see that the general fact 

 shown by the table is that the dominance of 

 control by slope a dominance always pro- 

 nounced is notably increased by increase of 

 slope, discharge, fineness, or form ratio. 



- 



(74) 



SUMMARY. 



With debris of a particular size and a chan- 

 nel bed of a particular slope, there is a particu- 

 lar discharge which is barely competent to 

 cause transportation. With increase of dis- 

 charge above this barely competent disc harge, 

 there is a proportional addition to the stream's 

 potential energy. The relation of capacity to 

 discharge is formulated on the assumption that 

 the capacity is proportional to some power of 

 the added energy, and therefore to the same 

 power of the added discharge. As each grade 

 of debris is somewhat heterogeneous as to the 

 size of its grains, this assumed principle can not 

 be applied strictly; the practical assumption is 

 that capacity varies with a power of the differ- 

 ence between the discharge and a constant 



discharge, the constant being so chosen as best 

 to harmonize the data. 



By means of such formulation the data were 

 readjusted and the rate of variation of capacity 

 with discharge, or the index of relative varia- 

 tion, i,, has been computed for a variety of 

 conditions. It is found to be greater as the 

 slope of channel, the discharge, the fineness of 

 debris, and the form ratio are less. The aver- 

 age of the values computed lor laboratory con- 

 ditions is 1 .42 and the ordinary range is from 

 1.00 to 2.00. 



The rate at which the efficiency of the stream 

 and the duty of the stream's water vary with 

 discharge is denoted by an index which is less 

 by unity than that for capacity. Its average 

 is 0.42 and its ordinary range is from to 1.00. 



It has previously been shown that the corre- 

 sponding indexes showing the relation of 

 capacity to slope are larger. In other words, ' 

 capacity is more sensitive to changes of slope 

 than to changes of discharge. If relative sensi- 

 tiveness to the two controls be expressed by a 

 ratio, the average value of that ratio is 1.36. 

 The ratio varies with conditions, being rela- 

 tively large when slope, discharge, fineness, 

 and form ratio are relatively small. 



The primary adjustment of observations of 

 capacity, described in Chapter II, was an ad- 

 justment with respect to slope. The probable 

 errors computed from differences between ad- 

 justed and unadjusted values were influenced 

 by only a portion of the observational errors. 

 In readjusting values of capacity with respect 

 to discharge, another division of the observa- 

 tional errors was encountered and its import- 

 ance was estimated. The probable errors 

 computed from the results of the two adjust- 

 ments are believed to represent with sufficient 

 approximation the order of precision of the ad- 

 justed values of capacity, which constitute the 

 main body of data for the discussions of the 

 report. The order of precision is expressed by 

 saying that the average probable error of the 

 adjusted values is a little more than 3 per cent. 



