62 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



is in the curve for (7a), but its divergence is not 

 sufficient to throw it out of apparent harmony 

 with the series of points representing the 

 original observations. 



In order to exhibit further the properties of 

 the formulas, their curves were extrapolated in 



both directions from the locus BD. Table 6 

 contains the numerical data used in plotting 

 the extensions. Figure 20 gives the exten- 

 sions of the curves for slopes greater than 

 those of the experiments, and figure 21 the 

 extensions for smaller slopes. 



TABLE 6. Numerical data computed for the construction of curves in figures 20 and "21. 



zpoo 



1,500 



1,000 



I 2 3 4 5 6 7 8 



Slope 

 FIGURE 20. Extrapolated curves of f=/(S) for tentative equations of interpolation, and for slopes greater than 2.4 per cent. 



The approximate range of this series of 

 experiments is from a slope of 0.8 per cent to 

 one of 2.4 per cent. The extrapolated curves 

 pertain to slopes from 2.4 to 10 per cent and 

 from 0.8 to per cent. The prompt divergence 

 of the lines as they leave the locus to which 

 they were adjusted shows that they have 

 widely different values for purposes of extra- 

 polation, and therefore presumably for pur- 

 poses of interpolation. 



Attention being given first to the curves for 

 higher slopes (fig. 20), it will be observed that 

 four of them ascend with progressively increas- 

 ing rate. The curve of formula (1 1 a) ascends 

 continuously, but its rate of ascent changes 

 at the slope of 4.37 per cent from an increasing 

 rate to a decreasing rate. The curve of formula 

 (6a) exchanges its increasing rate of ascent for 

 a decreasing rate at the slope of 3.33 per cent, 

 attains a maximum at a slope of about 6 per 



