116 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



Inspection of the table shows that under 

 this special condition the index (1) varies in- 

 versely with discharge, (2) varies inversely 

 with fineness, and (3) varies both inversely 

 and directly with width. In all these respects 

 the variations are similar to those noted when 

 the constant condition is slope, but the rates of 

 variation are not the same. To illustrate the 

 differences in rate I introduce Table 20, in 

 which data of Table 19 are compared, in par- 

 allel columns, with similar data (from Table 

 15) conditioned by constant slope. The same 

 data are also presented graphically and with 

 some generalization in figure 36. On giving 

 attention to the first division of the table and 

 to the upper diagram, it will be seen that the 

 variation of the index with discharge is some- 

 what less when the constant factor is mode of 

 traction than when it is slope. The second 

 division and second diagram show that the 

 variation with fineness is also less for constant 

 mode of traction. The third division and 

 diagram indicate that the variation with width 

 of channel is of the same order of magnitude in 

 the two cases, but that for constant mode of 

 traction the minimum value of the index is 

 associated with greater width. 



The comparison does not indicate that the 

 condition of uniform mode of traction is 



FIGURE 36. Variations of >i under condition of uniform mode of trac- 

 tion ( T, T, T), and under condition of uniform slope (S, S, S). Ver- 

 tical distances represent i\, with a common scale but different zeros. 

 Horizontal distances represent, for the upper pair of curves, discharge; 

 for the second pair, logarithms of fineness; for the lower pair, width of 

 channel; the values Increasing from left to right. 



greatly to be preferred to that of uniform slope 

 as a basis for the extension of laboratory gen- 

 eralizations to large natural streams. 



TABLE 20. Relations o/i, to discharge, debris grade, and channel width, when conditioned (1) by a constant mode of traction 



and (2) by a constant slope. 



IN CHANNELS OP SIMILAR SECTION. 



THE CONDITIONS. 



It will be shown in the following chapter that 

 one of the important conditions affecting capac- 

 ity is the relation of stream depth to stream 

 width, or the form ratio E. The matter has, in 

 fact, already received some attention in con- 

 nection with the variation of a. Now, in each 

 observational series the width is constant while 

 the depth varies, so that the form ratio is a 

 variable. Its variations accompany and are 



inseparable from those of slope; and the varia- 

 tion of capacity (within an observational 

 series), which up to this point has been treated 

 as if it were purely a function of slope, is in 

 reality a function of slope and form ratio 

 jointly. To separate the two factors and there- 

 by discover the relation of capacity to slope for 

 streams of similar section, it is necessary to 

 bring together data obtained by use of troughs 

 with different widths, selecting points of two 

 or more adjusted series which are characterized 

 by the same ratio of depth to width. In every 



