104 TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



TABLE 15. Values of i lt the index of relative variation for capacity in relation to slope Continued. 



VARIATION OF THE INDEX. 



Each column of the table contains a set of 

 values of t t which pertain to the same grade, 

 fineness, width, and discharge and of which the 

 changes are related to slope only. In figure 31 

 a number of these sets are plotted in relation to 

 slope. The curves have a strong family like- 

 ness, arising from the fact that the data were 

 all adjusted by the sigma formula; but the 

 likeness would not altogether disappear if the 

 assumptions of that formula were abandoned. 

 The general relations of -the index to slope are 

 as follows: 



(1) It varies decreasingly with slope. 



(2) Its rate of change is greater for low 

 slopes than for high. 



The upper group of curves all pertain to 

 grade (C) and width 1.00 foot, but represent 

 different discharges. They show (3) that the 

 rate of change for similar slopes is greater for 

 small discharges than for large. 



The second group of curves all pertain to 

 grade (C) and discharge 0.363 ft. 3 /sec., but 

 represent different widths. They show (4) 

 that the rate of change for similar slopes is 

 greater for broad channels than for narrow, or, 



as the depth varies inversely with the width, 

 that the rate of change is greater for shallow 

 streams than for deep. 



The third group of curves all pertain to 

 width 1.00 foot and discharge 0.363 ft. 3 /sec., 

 but represent different grades of debris. They 

 show (5) that the rate of change is greater for 

 coarse debris than for fine. 



In the third group the curves for grades (A), 

 (B), (C), (D), and (E) lie close together, while 

 those for the coarser grades (F) and (G) are 

 well separated. This is probably connected 

 with the fact that the range of fineness grad- 

 ually increases from (A) to (E) and then drops 

 abruptly from (E) to (F). The influence of 

 increasing range approximately neutralizes 

 that of decreasing fineness, and the inference 

 is (6) that the rate of change in the index is 

 greater for small range than for large. 



Consider now the variations of the index in 

 relation to width. In figure 32 (p. 106) the 

 ordinates, as before, represent values of \ and 

 the abscissas represent width of channel. The 

 points fixed by the data are shown by the dots. 



(7) The upper group of curves all pertain to 

 grade (C) and discharge 0.182 ft. 3 /sec., but rep- 

 resent different slopes. Their common char- 



