158 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



of nine are 5.31 and 5.04. Again the greater 

 mean is associated with the smaller discharge, 

 and the same relation is found by other com- 

 binations. The partial means resulting from 

 these reductions are arranged in the upper divi- 

 sion of Table 47. The general fact exhibited is 

 that the index, other conditions being the same, 

 varies inversely with discharge. 



The same method was employed to discover 

 the nature of the control of the index, first, by 

 grade of d6bris and, second, by width of chan- 

 nel; and the partial means are grouped in the 

 middle and lower divisions of Table 47. Of 

 the eight pairs of means connected with grade, 

 seven agree in testifying that the index varies 

 inversely with fineness. The exceptional testi- 

 mony comes from the comparison of grades (B) 

 and (C) ; and although it is emphatic, it serves 

 rather to illustrate the general discordance of 

 data from the experiments with grade (B) 

 than to qualify the general law as to the index. 



TABLE 47. Partial means based on Table 46, illustrating 

 the control of lyq, by discharge, fineness, and width. 



Of the five pairs of means connected with 

 width, three show increase of the index with 

 increase of width and two give the opposite 

 indication. The contrasts are not strong in 

 any case, and the nature of the law is not clear. 



It may be that the normal variation with 

 width is so slight as to be masked by accidental 

 errors of the data; or it may be that the index, 

 like the constant a, is a minimum function of 

 form ratio. 



By dividing the slope interval covered by a 

 computed value of the index and computing 

 separately the indexes for the two subintervals, 

 it was found that the index associated with the 

 higher slopes has a smaller value than that for 

 the lower slopes that is, the index varies 

 inversely with slopes. 



To compare the control of capacity by mean 

 velocity with its control by slope the 73 values 

 of I w (the synthetic index of relative variation 

 of capacity and slope, under condition of con- 

 stant width) corresponding to the tabulated 

 values of I r <t were computed. Each value of 

 I v <t is greater than the corresponding value of 

 /, the ratio ranging from 1.4 to 4.0. The 

 mean of 73 values of I v <i is 5.33; the mean I w 

 is 2.05; and the ratio of the means is 2.60. It 

 is in general true that the greater the indexes 

 the greater the ratio between them. 



In Table 48 means of the two indexes are 

 shown for the several grades of debris. Each 

 index varies with fineness and so, too, does the 

 ratio of indexes. 



TABLE 48. Synthetic indexes, comparing the control of ca- 

 pacity by -mean velocity loith the control by slope, and com- 

 paring both controls with grades of debris. 



MEAN VELOCITY VERSUS SLOPE. 



The comparison of I V(t with I w affords, 

 incidentally, an estimate of the relative varia- 

 tion of mean velocity and slope. The rate of 

 variation of capacity with mean velocity being 

 IVQ, the rate of variation of mean velocity with 

 capacity is I//F; and the rate of variation of 

 capacity with slope being I w , the rate of 

 variation of mean velocity with slope is 



