108 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



two do not exceed the computed probable 

 errors of the data, and the third is connected 

 with a value of \ to which the lowest weight 

 is ascribed. 



(14) The rate of change in the index is 

 greater for small discharges than for large. 



(15) For the same discharges the rate of 

 change in the index is greater for wide chan- 

 nels than for narrow, and is therefore greater 

 for shallow streams than for deep. 



FIGURE 34. Variations of ii in relation to fineness of de"bris. 



The curves of the lowest group all pertain to 

 width 0.66 foot and slope 1.8 per cent, but 

 differ as to grade of debris. They indicate 

 that 



(16) The rate of change in the index is 

 greater for coarse debris than for fine. The 

 peculiarities of spacing, as in a previous in- 

 stance, may show the influence of the factor of 

 range in fineness within the several grades. 



To consider now the relations of the values 

 of \ to the fineness of debris, the comparison is 

 made with linear fineness instead of bulk fine- 

 ness, as in discussing a, and it is found con- 

 venient to plot the logarithms of the quantities 

 instead of the quantities themselves. In figure 



34 the curves of the upper group are derived 

 from experiments conducted with a trough 

 width of 0.66 foot, and each one pertains to a 

 particular combination of slope and discharge. 

 Those of the second group are derived from ex- 

 periments with a trough width of 1 foot. 



(17) In the main they show decrease of i t 

 with increase of fineness, but the finer grades 

 give the opposite indication. The data are not 

 sufficiently harmonious to determine whether 

 the law of change is continuous or involves a 

 reversal. If it is continuous, i { is an inverse 

 function of F. 



In view of the fact that the double variation 

 of \ in relation to width is a complicating factor 

 and of the further fact that that variation is 

 less pronounced with high slopes than with low, 

 two curves (the lowest group of fig. 34) were 

 constructed from data pertaining to the highest 

 practicable slope, 2.4 per cent. Each curve 

 belongs to a particular width of trough, and 

 each is a composite with respect to discharge. 

 Their indication is practically the same as that 

 of the other groups. 1 



The character of the material has not seemed 

 to warrant a quantitative discussion of the 

 variations of the index of variation, and a sum- 

 mary of the qualitative discussion is neces- 

 sarily limited to generalities. The index of 

 relative variation or the sensitiveness of capac- 

 ity for traction to change of slope is a decreas- 

 ing function of the slope, the discharge, the 

 fineness of debris, and the range of fineness 

 and is a minimum function of width of channel. 



In symbols, 



!=/$,& F,&,w) --- ..... (39) 



If we assume tentatively that the function re- 

 placing i t in the exponent is the product of 

 functions of the individual conditions that is, 

 if we write 



then we must also recognize that in /,(),/, is 

 itself a function of Q, F, H, and w, that f u is a 

 function of F and w, and that/ v is a function of 



i Tn the data on flume traction the relation of capacity to fineness 

 exhibits peculiarities quite analogous to those here found in the relation 

 of ti to fineness. The capacity is larger for very fine and very coarse 

 d<5bris than for intermediate grades. A tentative explanation (see 

 Chapter XII) connects the larger capacity for fine debris with a tradi- 

 tion in process from traction to suspension. 



