RELATION OF CAPACITY TO SLOPE. 



117 



such comparison the capacity and slope asso- 

 ciated with the narrower trough are relatively 

 large, while for the wider trough they are rela- 

 tively small. The opportunities for comparison 

 are not abundant, because in the main the 

 observational series which are of like conditions 

 except as to width do not overlap in respect 

 to form ratio. 



SIGMA AND THE INDEX. 



In the records of the main body of experi- 

 ments 24 cases of overlap are found, all asso- 

 ciated with the finer grades of debris, from (A) 

 to (D). In each of these the comparison in- 

 cludes two widths only, no instance occurring 

 in which it can be extended to three. There 

 is, however, a special group of experimental 



series, planned in part for this particular pur- 

 pose, in which the trough-width interval is so 

 small that triple overlaps occur. The special 

 experiments were made with debris of grade 

 (C); the trough widths were 1.0, 1.2, 1.4, 1.6, 

 1.8, and 1.96 feet; and the experiments yield 

 nine triple overlaps. In six of these the extent 

 of overlap is such that numerical comparisons 

 have been made for more than one value of R. 

 With the aid of the computation sheets 

 described on page 95, a table was compiled in 

 which adjusted capacities and slopes were 

 arranged with respect to form ratio, and in 

 this table, which has not been printed, the 

 matter of overlaps was canvassed. Table 21 

 contains the data involved in the triple 

 overlaps. 



TABLE 21. Selected data, for grade (C), shewing the relation of capacity to slope when the form ratio is constant. 



To illustrate the use made of such data, the 

 case of #=1.119 ft. 3 /sec. and 5 = 0.15 is 

 selected. In that example the values of 

 slope and capacity are given for the trough 

 widths 1.4, 1.6, and 1.8 feet. These values 

 come from three adjusting equations, which are, 

 for the widths severally, =386 (S-0.08) 1 - 72 , 

 (7=400 (S-O.IO) 1 - 60 , and (7=430 (S-0.12) 1 - 67 . 

 The graphs of the equations are shown in 



figure 37. On each graph is a dot indicating 

 the point which corresponds to the tabulated 

 values of C and S, and for each of these points 

 the ratio R is 0.15. The curves represent the 

 relations of C to S under the condition of 

 uniform width. The three dots are points on 

 an undrawn curve to express the relation of 

 C to S under the condition of constant form 

 ratio. 



