184 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



the control of capacity by fineness would be 

 quite different if a different scale were used. 

 If, for example, mean linear fineness had been 

 defined as the arithmetical mean of linear fine- 

 nesses, the curve for linear fineness in figure 63 

 would be a straight line, while the line for bulk 

 fineness would be a curve similar to that shown 

 for linear fineness but turned through 180. 



When the fineness of the tractional load of a 

 stream is to be determined by means of a sam- 

 ple of the d6bris const ituting its bed, account 

 must be taken of another factor. Omitting 

 considerations affecting the selection of a sam- 

 ple, which belong to Chapter XIII, let us as- 

 sume that the sample hi hand is representative 

 of the stream's tractional load. In addition 

 to the debris which was carried along the bed, 

 it inevitably includes finer material which was 

 carried in suspension. Suspended particles are 

 arrested along with the coarser and form part 

 of every stream deposit. Once lodged in the 

 interstices of coarser particles, they are shel- 

 tered from the current and are not again dis- 

 turbed so long as the coarser material remains. 

 If the deposition of the coarser debris is very 

 rapid the amount of entangled finer stuff may 

 be small, but when deposition is slow the inter- 

 stices act continuously as traps and catch sus- 

 pendible debris until they are filled. The lat- 

 ter is the usual condition, and the tractional 

 sample therefore ordinarily contains a consid- 

 erable percentage of suspensional material. 

 To separate the two it is necessary to draw an 

 arbitrary line, for the graduation in fineness is 

 complete. As regards interstitial space, the 

 tractional part of the sample is comparable with 

 the more complex mixtures of the laboratory, 

 and its voids may be estimated as 25 per cent 

 of the whole space. The suspensional d6bris 

 packed in these voids may be assumed itself 

 to include 25 per cent of voids, so that the net 

 volume of its particles is three-fourths that of 

 the containing voids, or 18.75 per cent of the 

 whole space. The net volume of the trac- 

 tional particles being 75 per cent of the whole 

 space, the two divisions of the sample bear the 

 relation, by net volume or by weight, of 75 to 

 18.75, or of 4 to 1. This gives a practical rule 

 for separation. The sample should be divided, 

 with aid of sieves and scales, into a coarser four- 

 fifths and a finer one-fifth, and only the coarser 

 part should be used in estimating mean fine- 



ness. In figure 65 the entrapped suspensional 

 material is represented by the triangular area 



ODE. 



SUMMARY. 



The purpose of the experiments with mix- 

 tures was to bring the results from work with 

 separate grades into proper relation with 

 phenomena of unsorted natural material. The 

 indications given by these experiments are in 

 part direct and in part conditioned by the 

 principle adopted in framing a scale of fineness. 

 The adopted principle makes the conception of 

 bulk fineness fundamental and that of linear 

 fineness derivative. 



The capacities for traction observed in the 

 experiments with narrowly limited grades are 

 less than for equivalent grades with greater 

 diversity in fineness. A study of data from 

 mixtures of two narrow grades indicates that 

 the ratio of advantage for diversified debris is 

 from 1.17 to 2.22, the mean of five estimates, 

 from different groups of data, being 1 .66. Two 

 comparisons of results from highly diversified 

 grades, with results from nearly homogeneous 

 grades of the same fineness, give as estimates 

 of the ratio of advantage 1.15 and 1.17. The 

 larger estimates were made by an indirect 

 method but are independent of the scale of 

 fineness. The smaller estimates were made 

 by a direct method but involve the theory of 

 the scale of fineness. In combining the two 

 groups of estimates, greater weight is assigned 

 to the smaller, not because they are of recog- 

 nized higher authority, but because the same 

 scale of fineness will almost necessarily be 

 used in applying the results of the investiga- 

 tion to practical questions. The compromise 

 value of 1.2 is adopted, as a correction to be 

 applied to values of capacity in Table 12 in 

 estimating capacities for diversified grades of 

 like fineness. 



The advantage of diversification appears to 

 arise largely from the fact that the finer 

 particles, by filling spaces between the coarser, 

 make a smoother road for the travel of the 

 coarser, and it is not proved that a highly 

 diversified debris gives higher capacity than 

 one containing only two sizes of particles. 



It is especially notable that when fine ma- 

 terial is added to a previously homogeneous 

 coarse material not only is the total capacity 

 increased, but the capacity for the coarser part 



