118 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



It is convenient, in discussing this undrawn 

 curve, to assume that its equation involves a 

 and is otherwise of the same type as the equa- 

 tions used in discussing the data for constant 

 width. In this case, moreover, the assump- 

 tion is countenanced by the fact that traction 

 is limited by the competent slope. By making 

 the assumption, it is possible to compute all 

 the parameters of the curve from the coordi- 

 nates of the three known points and write its 

 equation : 



=469 (S -0.23) '- 25 (43) 



In the present connection the most significant 

 of the parameters is o\ and the values of a 



have been computed for each of the cases of 

 Table 21. They are assembled in Table 22. 



TABLE 22. Values of a corresponding to data in Table SI. 



400 



a 

 to 

 <J 



Slope 



FIGUHE 37. Curves of C /(S) for trough widths of 1.4, 1.6, and 1.8 feet, showing points which agree as to form ratio. 



Grade (C). Q-1.119ft.3/sec. fi-0.15. 



One value of a has a negative sign. As this 

 yields positive capacity for negative slope, 

 thus transcending the physical conditions of 

 traction, and as the value is numerically large, 

 an error of importance is betrayed. The 

 error appears not to be one of computation 

 and must be ascribed either to the observa- 

 tional data or to assumptions made in the 

 work of reduction and adjustment. In either 

 case its existence serves to qualify the values 

 of a as of low precision. 



In view of that qualification, the study of the 

 values of a in detail appears unprofitable and 

 only their mean will be considered. In deriv- 

 ing the general mean a subsidiary mean was 

 first found for each case of overlap and these 

 were afterward combined, this course being 

 followed because when several values of a are 

 derived from the same overlap of series the}* 

 are not independent. The general mean thus 

 derived is +0.08, and this may be compared 

 with a mean similarly obtained from the asso- 



