100 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



and develop the value of i t from equation (10). 

 The logarithmic equivalent of (10) (p. 64) is 



log C"=log 6,+nlog (S-a) (15) 



Differentiating, and dividing both -members by 

 d log 8, 



Introducing these values in (37) and reducing, 

 we have 



tl ~S-<j' 



(38) 



.(37) 



d log G = n d\og(S-a) 

 d log S d log S 



The first member of this equation is the value 

 of i l} and i t may be substituted for it. Also 



and 



The values of n and a being known for each 

 observational series, it is possible, by means of 

 equation (38), to compute \ for any value of S. 

 The values of i l have been computed for series 

 of values of S having the uniform interval of 

 0.2 per cent (and below 1.0 per cent the inter- 

 val of 0.1 per cent) and having such range in 

 each observational series as to correspond with 

 the range of the observations. These values 

 are recorded in Table 15. It is proposed to 



,, o _dS discuss their relations to various conditions, 



S beginning with slope. 



TABLE 15. Value* ofi lt the index of relative variation for capacity in relation to slope. 



dlog (S-a)= 





