154 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



are given in Table 15. They have been copied 

 into Table 45, so as to be conveniently com- 

 pared. 



Inspection shows that i t is in general much 

 smaller than \ but that it becomes greater as 

 the limit of competence is approached. As to 

 the first of these generalizations there can no 

 question, but the second is not equally satis- 

 factory. In the vicinity of competence the 

 value of i t is highly sensitive to the influence 

 of <f>; and in the same region \ is highly sensi- 

 tive to a. The features of the table might be 

 produced by slight overestimates of <f> or by 

 slight underestimates of a. In view of this 

 consideration it is probably best to leave the 

 higher values of the index out of the account 

 and base a computation of averages wholly on 

 the lower values. Including only the 28 values 

 of each index associated with grades (A) to (F), 

 the means are, for i t 0.77, for i t 1.79; and the 

 ratio of the second to the first is 2.4; that is, 

 the sensitiveness of capacity to control by slope 

 is estimated to be 2.4 times as great as its sen- 

 sitiveness to control by fineness. The ratio of 



sensitiveness for slope and discharge iji 3 having 

 been estimated at 1.36, it follows that the ratio 



2 4 

 for discharge and fineness is =-55 1.8. 



Mean i t : mean i s : mean i t : : 2.4 : 1.8 : 1.0. 



It is to be understood that these estimates 

 are of the most general character. The ratios 

 doubtless vary notably with conditions. 



The property with which capacity has been 

 compared in this chapter is linear fineness, F, 

 defined as the reciprocal of diameter, or as the 

 number of grains to the linear foot. Bulk fine- 

 ness, F 2 , defined as the reciprocal of volume, is 

 proportional to the cube of linear fineness. It 

 follows that the index of relative variation 

 when capacity is compared with bulk fineness 

 is one-third the corresponding index, i t , for 

 capacity and linear fineness; and the same 

 factor applies to synthetic indexes. If bulk 

 fineness were substituted for linear fineness in 

 equations of the form of (75), the values of <f> 

 would be quite different and the values of p 

 would be uniformly one-third as great. 



DUTY AND EFFICIENCY. 



The relations of duty and efficiency to ca- 

 pacity involve discharge and slope but are in- 

 dependent of fineness. Fineness, therefore, has 

 exactly the same control of duty and efficiency 

 that it has of capacity, and the conclusions of 

 this chapter apply without qualification to duty 

 and efficiency. 



SUMMARY. 



Capacity for traction is greater for fine d6bris 

 than for coarse that is, capacity increases with 

 fineness. The law of increase admits of formu- 

 lation in a manner strictly analogous to that 

 employed in comparing capacity with slope 

 and discharge that is, it is found that ca- 

 pacity varies approximately with a power of 

 the fineness less a constant fineness. The value 



of the constant finenes3 varies with conditions, 

 being greater as slope, discharge, and form 

 ratio are greater. The rate at which capacity 

 varies with change of fineness, or the index of 

 relative variation, is not the same for all 'con- 

 ditions, being greater as slope, discharge and 

 form ratio are less. Under similar conditions 

 the rate is less than the corresponding rate for 

 capacity and slope, the average ratio between 

 them being as 1 to 2.4. 



The arrangement of capacities in accordance 

 with the assumed law of increase develops dis- 

 crepancies which are believed to be of the na- 

 ture of systematic errors. The largest of these 

 have a magnitude of about 10 per cent. They 

 are tentatively ascribed to peculiarities of the 

 <16bris used in experiments and to imperfectly 

 developed laboratory methods. 



