182 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



limited in the opposite direction by competent 

 fineness for suspension, the area GED repre- 

 senting suspendible material entangled with 

 the bed load. The mean fineness of the trac- 

 tional load is marked at M. 



In sorting debris for the laboratory experi- 

 ments, the material of the river's load was 

 divided by sieves, and this partition might be 

 represented in the diagram by a series of 

 vertical lines slightly flexed to take account 

 of the influence on the separation of irregularity 

 in shape of particles. The shaded areas X and 

 Y may represent the constitution as to fineness 

 of two of the sieve-separated grades. 



The experiments show that for a narrowly 

 limited grade, such as X or Y , which has the 

 same mean fineness as the river alluvium, 

 ABOD, the capacity for traction is much less 

 than for the alluvium. They indicate also, 

 though less decisively, that for a nearly equal 

 mixture of a fine grade with a coarse, both 

 being narrowly limited, the capacity is nearly 

 the same as for the unsorted alluvium, pro- 

 vided the mean fineness is the same. The 

 essential property appears to be abundance of 

 both coarse and fine, and not multiplicity of 

 grades of fineness. 



Passing now from capacity to capacity's 

 rate of variation in respect to fineness or to 

 the valuation of i t , we find a certain parallel- 

 ism. For the narrowly limited grades the 

 sensitiveness of capacity to fineness, as meas- 

 ured by the index i 4 , extends upward from 

 about 0.60; while values of the synthetic 

 index, I t , range from 0.70 to 1.00 or more. 

 As to these values the data are not abundant. 

 For mixtures of two narrow grades we have a 

 few estimates of I t> of which the largest is 0.70; 

 and for grades similar to ABCD a single weak 

 estimate of 0.57. If we conclude that the 

 sensitiveness of capacity to fineness is less for 

 natural grades than for the narrowly limited 

 grades, we must base the inference almost 

 wholly on the data from the mixtures of two 

 grades, connecting the latter with natural 

 grades by aid of the analogy outlined above. 

 This I am willing to do, but at the same time I 

 would record my recognition of the weakness 

 of the evidence and reasoning. It is estimated 

 that, on the average, the capacity of streams 

 for natural grades of debris varies with the 

 0.60 to 0.75 power of linear fineness. This is 

 equivalent to saying that capacity varies with 



the 0.20 to 0.25 power of bulk fineness, or 

 with the fifth or fourth root of bulk fineness. 



While the curve in figure 65 is based on the 

 mechanical analysis of material which consti- 

 tuted the tractional load of a river current, 

 there is no reason to believe that its form pre- 

 sents a dominant type. Inspection of other 

 analyses, in fact, suggests that such curves ex- 

 hibit much variety and may sometimes even 

 present two maxima. The load which a natu- 

 ral current carries is determined not only by 

 the two limits of competence, but by the char- 

 acter of the material within its reach. Neigh- 

 boring affluents of a river may bring to it 

 strongly contrasted grades of debris, or their 

 tribute may at one time be much finer than at 

 another. Moreover, a river is not a simple cur- 

 rent, but a complex of currents, which vary in 

 competence and in the character of their loads. 

 It is true that, the channel being considered as 

 a whole, its load at one point is essentially the 

 same as just above or just below, but the mode 

 of movement involves a continual remodeling 

 of the bed and a sorting and re-sorting of the 

 material. The load at any particular point 

 and time is conditioned by many factors of the 

 complex. For this reason a representative 

 sample of a river's load is not easy to define or 

 to collect. 



In view of this complexity it is difficult to 

 apply even a simple formula to problems in 

 river engineering, and refinement in formula- 

 tion would be of little avail. For the same 

 reason it is not practicable to derive a formula 

 directly from river data, and the product of 

 the laboratory is the best available, despite the 

 artificial simplicity of its conditions. 



DEFINITION AND MEASUREMENT OF MEAN 

 FINENESS. 



The term "mean fineness/' as here used, is 

 not free from the possibility of misapprehen- 

 sion. As the fineness of d6bris is a property 

 depending on the size of component particles, 

 it is not unnatural to think of fineness as a 

 property of the particles and there is, for that 

 matter, a fineness of particles. To obtain the 

 mean fineness of particles, one would first de- 

 termine the finenesses of the individual parti- 

 cles, and then the mean of those finenesses. 

 The basal unit would be the particle. In de- 

 riving the mean fineness of a body of debris 

 the basal unit is some unit by which quantity 



