APPLICATION TO NATURAL STREAMS. 



235 



excluded from the other is the finer part of the 

 suspended load, the part that does not sink to 

 the bottom so long as the current is sufficiently 

 active for traction. Being purely suspensional, 

 its quantity is peculiarly a function of supply 

 and is connected with discharge only through 

 the association of discharge with rain. Wher- 

 ever discharge is largely a matter of tribute 

 from snowbanks, the suspended load is con- 

 spicuously independent of discharge. 



If we exclude from view the purely suspen- 

 sional material, a natural criterion for inclusion 

 is the finest debris which low-stage discharge 

 moves by traction, and as low-stage traction is 

 limited to the bars, or interpool shoals, it is 

 the finest tractional debris of those shoals. If 

 we consider a gradual increase of discharge from 

 least to greatest, we have at first no traction. 

 Then for a particular discharge, which may be 

 called the competent discharge, traction begins 

 on the shoals, only the finest of the de'bris being 

 moved. Gradually coarser and coarser mate- 

 rial is included, the range in fineness and the 

 load increasing together; but in this phase of 

 action the load is not necessarily the equiv- 

 alent of the capacity, for it may be limited by 

 the supply of de'bris of requisite fineness. 

 After a time another critical discharge is at- 

 tained, which initiates the loaning of de'bris 

 from traction to suspension, and thereafter a 

 constantly increasing share of the traveling 

 de'bris is suspended. As the suspended parti- 

 cles travel faster than the saltatory, and as 

 capacity is the ability of the stream, measured 

 in grams per second, to move de'bris past a 

 sectional plane, the transfer from traction to 

 suspension is an important factor in the en- 

 hancement of capacity. 



The relation of capacity to discharge, con- 

 templated from this viewpoint, has two ele- 

 ments in common with the discharge factor of 

 the laboratory formula. It includes a compe- 

 tent discharge, corresponding to the zero of 

 capacity, and it associates continuous increase 

 of capacity with continuous increase of dis- 

 charge. It differs, however, in important ways, 

 and the possibility of expressing it by a definite 

 formula is not evident. In the pool and rapid 

 phase of activity the supply of de'bris suitable 

 for traction is usually limited, and in many 

 streams it is exhausted during each recurrence 

 of the phase. In the phases of greater dis- 

 charge, when traction occurs in the deeps as 



well as on the shoals, the sequence of capacities 

 depends not only on discharge but on the rela- 

 tive proportions of debris of different grades of 

 fineness in the material of the load. It is prob- 

 able that for most streams the load-discharge 

 function is discontinuous at the limit of the 

 pool and rapid phase. 



Because of this presumable discontinuity, 

 because the tractional work while the pools 

 exist accomplishes only a local transfer of 

 de'bris, and because the work performed is 

 usually of negligible amount in comparison 

 with the work of larger discharges, it is prob- 

 ably better to ignore altogether the pool and 

 rapid phase in any attempt at general formu- 

 lation. If that be left out of account and if 

 the general features of the laboratory formula 

 be retained, the constant becomes the dis- 

 charge which initiates traction in the deeps, 

 and thus initiates through transportation of 

 bottom load. If we accept that as a starting 

 point, the material so fine as to be suspended 

 by that discharge may be classed as purely sus- 

 pensional, and other material suspended by 

 larger discharges may be grouped with the 

 tractional load. For the tractional load thus 

 enhanced, or the amplitractional load, as it 

 may conveniently be called, the rate of varia- 

 tion with discharge is evidently higher than 

 the rates found for simple grades in the labora- 

 tory, and it may be much higher, for the de'bris 

 diverted from traction to suspension, instead 

 of lagging behind the lowest and slowest 

 threads of the current, now speeds with the 

 current's mean velocity. 



It is possible that a practical formula for the 

 fluctuations of an alluvial river's load may fol- 

 low these lines, taking the form 



where C a is the capacity for amplitractional 

 load, and K, is the smallest discharge competent 

 to establish a continuous train of traction 

 through deeps and shoals; but the suggestion 

 as to form has no better basis than analogy, 

 and no data are known tending to determine 

 the magnitude of the important parameter o. 



THE FINENESS FACTOR. 



When the work of two natural streams is 

 compared and the streams are of the same type, 

 it i-i believed that the fineness factor of the 



