RELATION OP CAPACITY TO DISCHAKGE. 



147 



i a mentioned on page 143 were contrasted with of the three groups indicates that the ratio 

 corresponding values of i,. The results are of the indexes increases with increase of 

 summarized in Table 40, below, in which each slope. 



TABLE 39. -Variations of the indexes i t andi 3 , and their ratio, in relation to fineness of debris. 



TABLE 40. Variations of the indexes i t and tj, and their ratio, in relation to slope. 



To sum the results of the preceding para- 

 graphs: The sensitiveness of capacity for trac- 

 tion to changes of slope, as measured by the 

 exponent i lt is in general greater than its sen- 

 sitiveness to changes of discharge, measured 

 by ig. The superiority of the control by slope 

 persists through nearly (or perhaps quite) the 

 entire range of conditions realized in the 

 laboratory. If the superiority is measured by 



m 



the ratio ^, its average value (based on 64 com- 



** 



parisons) is 1 .36, and it increases with increase 



of slope, discharge, form ratio, and fineness of 

 debris. 



(72) 



Another mode of comparing the controls by 

 slope and discharge is by means of the syn- 

 thetic index of relative variation (p. 99), and 

 in some respects this mode is more satisfactory 

 than the one given above. The synthetic index, 

 7 3 , of the relative variation of capacity and dis- 

 charge was computed for 21 cases, in each of 

 which the greater discharge was approximately 



double the lesser. The synthetic index / of 

 the relative variation of capacity and slope, 

 was computed for 21 pairs of cases, the greater 

 slope being double the lesser. Each value of 7 S 

 was joined to two discharges and a slope and 

 associated with a pair of values of /,. Each of 

 the two values of 7 t was joined to one discharge 

 and two slopes, the slopes being so chosen, 

 whenever possible, that their mean coincided 

 with the slope of the associated 7 3 . The mean 

 of the 42 values of 7 t is 1.92; that of 21 values 

 of 7 3 is 1 .42 ; and the ratio of these means is 1 .35. 

 The result is practically identical with that 

 obtained by the discussion of values of i t and i 3 . 



CONTROLS OF DUTY. 



The index of relative variation of the duty 

 of water in relation to slope (p. 121) is i lr the 

 same as the index for capacity and slope. 

 The corresponding index for the duty of water 

 in relation to discharge (p. 144) is i 3 1. The 



rt 



ratio of these indexes, - , is evidently greater 

 i 3 



n 



than the ratio -r, which has just been consid- 



