134 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



SPECIAL GROUP OF OBSERVATIONS. 



The special group of observations recorded 

 in Table 4 (I), page 51, were arranged largely 

 for the purpose of defining p, the optimum form 

 ratio. They differed from the main body of 

 observations in that the interval between the 

 discharges employed and the interval between 

 the widths employed were both smaller; and 

 they were restricted to a single grade of debris. 

 They had the advantage of an experimental 

 method believed to be the best developed in the 

 laboratory; and in view of this advantage their 

 series were constituted of fewer individual ob- 

 servations than those of the main body of ex- 

 periments. The results have not been satis- 

 factory, and attempts at formulation in the 

 present connection have developed marked in- 

 congruities. In figure 46 three curves are 

 given, and the corresponding numerical data 

 appear in Table 30. Each curve is based on 

 five observational points, but they are so irregu- 

 larly placed that their control is feeble. 



On comparing the two cases having the 

 same discharge, it is seen that the greater 

 slope is associated with the smaller values of 

 m, p, and a and with the greater value of & 2 , 



the difference being most strongly marked for 

 m and p. On comparing the two cases having 

 the same slope, it is seen that the greater dis- 



300- 



300 



S'l.l 

 q '1.H9 



FIGUBE 46. Relation of capacity, C, to form ratio, R. Variation of 

 the function C=b?(l aK)Em with slope and discharge. Data from 

 special group of experiments with debris of grade (C). Scale of C 

 vertical; scale of R horizontal. 



charge is associated with the smaller values of 

 m and p and with the larger value of 6 2 , while 

 the values of are nearly equal. 



TABLE 30. Observed and computed quantities illustrating the influence of slope and discharge on the relation of capacity 



to form ratio. 



SUMMARY AS TO CONTROL BY CONDITIONS. 



The treatment of the observational data by 

 means of a formula specially designed to show 

 the relation of capacity for traction to the 

 proportions of the cross section develops 

 incongruities. These are of such distribution 

 as to indicate that they are due in chief part 

 to the observations and their methods of 

 adjustment. Discrepancies which manifestly 



pertain to the data are so large that it is not 

 practicable to determine whether the imper- 

 fections of the formula are important. 



The exponent m varies inversely with slope, 

 with discharge, and with fineness. Thus all 

 the conditions which tend to increase capacity 

 tend also to make capacity less sensitive to 

 changes in form ratio. 



The optimum form ratio, p, varies inversely 

 with slope and with fineness. As to its varia- 



