180 



TRANSPORTATION OF DEBKIS BY RUNNING WATER. 



FINENESS. 



A similar attempt was made to correlate the 

 capacity curves of figures 55 and 56 with fine- 

 ness. In computing the fineness of a mixture, 

 the finenesses of its components were used as 

 data, and the combination was made with bulk 

 finenesses (p. 21) as follows: Denoting the pro- 

 portions of components by a, b, c, etc., their 

 bulk finenesses by F 2 ', F 2 ", F 2 ", etc., and the 

 fineness of the mixture by F 2 m , 



....(85) 



a + b + c + etc. 



Linear fineness, F, was then computed by 

 formula (88). 



The results are listed in Table 63, together 

 with the corresponding capacities for traction 

 when the discharge is 0.363 ft. 3 /sec. and the 

 slope is 1.4 per cent. 



TABLE 63. Finenesses of mixed grades and their components. 

 [Computed from data in Tables 1, 4 (J), and 4 (K).] 



The comparisons of capacity with fineness 

 for series of mixtures of two grades are illus- 

 trated by figure 63, where the horizontal scale 

 is that of the proportions of fine and coarse in 

 the mixture. The capacity curve is identical 

 with the second in figure 55, and the other 

 curves pertain to the same series of (C G) mix- 

 tures. The curves for capacity and linear fine- 

 ness are strongly discordant, capacity changing 

 most rapidly with mixtures approximately in 

 the ratio of 1:1, and fineness changing most 



rapidly when the proportion of the finer grade 

 is minute. The graph of bulk fineness is a 

 straight line and betrays no sympathy with the 

 sigmoid curve of capacity, though somewhat 

 less discordant than the curve of linear fineness. 

 It is quite evident that the peculiar relation 

 of capacity to the pioportions of a binary mix- 

 ture is not to be either accounted for or formu- 

 lated as a relation of fineness, and we have just 

 seen that it can not be formulated in terms of 

 the percentage of voids. The elimination of 

 those two associated factors leaves it so far 

 as our recognized alternatives are concerned 

 to be ascribed wholly to modifications of the 

 texture of the channel bed and the consequent 

 modifications of the mode of transportation, 

 and to these factors it is not practicable to give 

 numerical expicssion. 



RELATION OF CAPACITY TO FINENESS, FOR 

 NATURAL GRADES. 



There is another way of comparing the ca- 

 pacities pertaining to mixed grades with the 

 fineness of the grades, which largely avoids the 

 influence of changing mode of traction and 

 which throws a side light on the relation of 

 capacity to fineness in the case of natural 

 grades. Instead of comparing the data for 

 different mixtures of the same two simple 

 grades, it compares data from similar mixtures 

 of different pairs of simple grades. 



Figure 64 has been compiled from data in 

 Table 63. Its upper group of five dots repre- 

 sents the logarithms of capacity in relation to 

 the logarithms of linear fineness, for combina- 

 tions of fine and coarse in the ratio of 4:1 

 (one ratio of 3:1 being included). The line 

 drawn among them gives, by its inclination, 

 an estimate of 7 4 , the synthetic index of 

 capacity in relation to fineness, for a range in 

 fineness from 166 to 908, the value being 0.70. 

 The next group of dots corresponds to mix- 

 tures of two fine to one coarse and gives 0.57 

 as a value of the index. The next group, dis- 

 tinguished by crosses, corresponds to mixtures 

 of one part fine with one of coarse. It includes 

 six points, but one of these stands far from the 

 line suggested by the others. The line, as 

 drawn, represents an index value of 0.62. In 

 the fourth group, distinguished by X's and 

 corresponding to mixtures of one fine to two 

 coarse, the points are so irregularly placed 

 that no line can be drawn; and a fifth group, 



