66 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



rithmic plots exhibit curvature so definitely 

 that the approximate magnitudes of the con- 

 stants necessary to eliminate it can be inferred. 

 In some of the remaining series the observa- 

 tions are not so distributed as to bring out the 

 curvature. For others the observational posi- 

 tions on the plots are too -widely dispersed to 

 give good indication of the character of the 

 best representative line. 



On the 30 logarithmic plots the curves ap- 

 proximately representing the observations were 

 drawn, and the values of a necessary to replace 

 the curves by straight lines were computed 

 graphically in the manner just indicated. 

 These values are given, to the nearest tenth of 

 1 per cent of slope, in Table 7, where they are 

 arranged with reference to the conditions of 

 the experiments. 



TABLE 7. Values of a in C=b l (Sa) n , estimated from logarithmic plots of observations. 



NOTE. The horizontal dashes indicate series of observations to which values of <r are to be assigned. 



The same table shows the distribution of the 

 experimental series which fail to give values of 

 a but to which it is proposed to assign values. 

 In order to assign these values properly it is 

 necessary to know the laws of variation of a 

 with reference to the conditions of experimen- 

 tation. These are suggested in part by the 

 roughly determined values of the table and 

 are otherwise indicated by general considera- 

 tions. The variations are connected with at 

 least three conditions discharge, width, and 

 fineness and are less surely connected with 

 range of fineness. 



Considering first the variation of a with dis- 

 charge and giving attention in the table to 

 values of a falling in the same horizontal line, 

 we find by inspection that invariably the value 



for a larger discharge is either less than or 

 equal to the value for the corresponding smaller 

 discharge. The indication is that a is a de- 

 creasing function of discharge. This relation 

 might have been inferred from general con- 

 siderations, on the theory that a represents 

 competent slope. Competent slope is the slope 

 giving competent velocity along the bed, but 

 bed velocity also varies directly with discharge. 

 With large discharge less slope is necessary to 

 induce competent velocity; with small dis- 

 charge more slope. In other words, compe- 

 tent slope varies inversely with discharge. In 

 a preliminary discussion of the traction data 

 for debris of grades (B) and (C) it was found 

 that capacity is more sensitive to changes in 

 slope than to changes in discharge. The rela- 



