KELATION OF CAPACITY TO FINENESS OF DEBRIS. 



151 



For any velocity, as determined by slope, 

 discharge, and width, there is a competent 

 fineness, marking the limit between traction 

 and no traction ; and to this extent, at least, the 

 relation of fineness to traction is analogous to 

 the relations of slope and discharge. It is not 

 easy to carry the analogy further, because slope 

 and discharge are conditions of active force, 

 and fineness is a condition, of reactive force, or 

 resistance; but an experiment in formulation 

 reveals a parallelism quite as striking as that 

 between the capacity-slope and capacity-dis- 

 charge functions. 



Assuming 



-(75) 



in which is a constant fineness and b t a con- 

 stant of the numerical value of capacity when 

 F= < + !,' the five sets of data in Table 44 

 were treated graphically for the determination 

 of <j> and p. The methods were such as have 

 already been described (pp. 65 and 139). The 

 formulas were then used to compute read- 

 justed values of capacity, C r , and values of the 

 index of relative variation, i t> and probable 

 errors were also computed. 



TABLE 44. Numerical data connected with the plots in figure SO, and illustrating the relation of capacity for traction to grades 



of debris. 



PRECISION. 



The average probable error of the read- 

 justed capacities was found to be 2.1 per 

 cent. This error is to be ascribed in part to 

 discordance of the data among themselves, and 



in part to discordance of the formula with the 

 data; but the distribution of the residuals is 

 not such as to imply important discordance of 

 the formula. 



i The dimensions of capacity are -M+i T-', and of fineness -*. The 

 constant 6 ( , being equal to C/ (F*t>)p, hag dimensions L+'P J/+' T~ l . 



