RELATION OF CAPACITY TO DEPTH. 



165 



The derivation of moans in Table 55 followed 

 the precedents of Tables 47 and 50. An ex- 

 amination of logarithmic plots shows that 7<j S 

 varies inversely, but only slightly, with dis- 

 charge. The means in Table 55 show that it 

 varies inversely with slope and fineness, but 

 they give no clear indication of its essential re- 

 lation to width. 



TABLE 55. Partial means based on Table 54, illustrating 

 the control of I ds , by slope, fineness, and width. 



For each of the 68 values of l ds , the corre- 

 sponding value of the synthetic index of the 

 relation of capacity to discharge, I 3 , was com- 

 puted, the relations being such that the paired 

 values represent exactly the same conditions. 

 It was found that, without exception, the values 

 of I ds are greater than the companion values 

 of 7 3 . Table 56 contains a series of compara- 

 tive means and their ratios, the ratio of general 

 means being 1.62. 



TABLE 56. Synthetic indexes, comparing the control of ca- 

 pacity by depth with the control by discharge, and comparing 

 ooth controls with grades of debris. 



DEPTH VERSUS DISCHARGE. 



The comparison of 7 ds with 7 3 affords, inci- 

 dentally, an estimate of the relative variation 

 of depth and discharge. The rate of variation 

 of capacity with depth being I ds , the rate of 

 variation of depth with capacity is 1/7^; and, 

 the rate of variation of capacity with discharge 

 being 7 3 , the rate of variation of depth with dis- 

 charge is 1 1 h a + 7 3 = 7 3 /7 ds . The values of I 3 /I ds 

 in Table 56 are therefore estimates of the varia- 

 tion of depth in relation to discharge, under the 

 limiting condition of constant slope. They are 

 of the quality of the synthetic index and are 

 based on the general range of conditions 

 realized in the laboratory, except those in the 

 neighborhood of competence. For this range 

 of conditions depth varies, on the average, with 

 the 0.62 power of discharge. 



WHEN VELOCITY IS CONSTANT. 



By interpolation from the data recorded in 

 Tables 12 and 14, values of capacity and depth 

 may be found corresponding to selected values 

 of mean velocity. Such values were derived 

 for mean velocities of 2, 3, and 4 ft./sec., and 

 from them were computed the 42 values of hv 

 in Table 57. 



TABLE 57. Values of I AV , the synthetic index of relative 

 variation for capacity in relation to depth of current, when 

 mean velocity is constant. 



Most of these values are negative, but nine 

 are positive. The mean of the 42 values, com- 

 bined with regard to sign, is 0.54. A posi- 

 tive value, considered by itself, indicates that 

 capacity varies directly with depth, and a nega- 

 tive value that the variation is inverse. At 



