160 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



THE SYNTHETIC INDEX WHEN DEPTH IS 

 CONSTANT. 



The capacities and mean velocities corre- 

 sponding to particular depths were derived from 

 the computation sheets described on page 95. 

 The selected depths were 0.10, 0.14, 0.20, and 

 0.28 foot, and the data available for these depths 

 afforded 32 values of the synthetic index, Ivd- 

 These arc recorded in Table 51, and partial 

 means derived from them are arranged in 

 Table 52 so as to show variation in relation to 

 fineness of debris and width of channel. 



TABLE 51. Values of Ira, the synthetic index of relative 

 variation for capacity in relation to mean velocity, when 

 depth of current is constant. 



TABLE 52. Partial means based on Table 51, illustrating the 

 control of I V t, by fineness and width. 



With a single exception in each group of 

 means, the indication is that the index varies in- 

 versely with fineness and directly with width. 

 Under the condition of constant depth each 

 change in mean velocity 13 accompanied by 

 changes of both slope and discharge, and the 

 influences of the two can not be examined sepa- 



rately. The features of the logarithmic plots, 

 not here reproduced, show that the index varies 

 inversely with slope and discharge, considered 

 together. 



THE THREE INDEXES. 



In bringing together the results outlined in 

 the preceding paragraphs we may replace width 

 of channel by form ratio, bearing in mind that 

 the two factors are so related that their varia- 

 tions are in opposite senses. So far as qualita- 

 tive statement is concerned, the three syn- 

 thetic indexes are identical in properties. The 

 sensitiveness of capacity for traction to the 

 control of mean velocity of current varies in- 

 versely with slope of channel, discharge, fine- 

 ness of debris, and form ratio. 



(81) 



As to the first three conditions the generaliza- 

 tion is unqualified, but it is possible that the 

 function as to form ratio is of the minimum 

 class instead of inverse. 



The three indexes are not of the same mag- 

 nitude. In comparing them Ira was made the 

 standard, partly because the values computed 

 for it are fewer. To compare with each of its 

 32 values, that value of Irs which most nearly 

 represents the same group of conditions was 

 selected, and also a pair of values of I v <t which 

 collectively represent nearly the same condi- 

 tions. Means were then derived for each index 

 for each of the six grades to which they pertain, 

 and also general means all of which are shown 

 in Table 53. In the same table are the ratios 

 between general means and also between the 

 corresponding grade means. For the general 

 means I r<i is 7 per cent greater than I Y d, and 7r 

 is the greater for all the partial means but one. 

 For all the partial means but one I V s is smaller 

 than Ivd, and for the general means it is 9 per 

 cent smaller. Capacity is most sensitive to 

 the mean velocity conditioned by constant dis- 

 charge and least sensitive to the mean velocity 

 conditioned by constant slope. 



These results have a theoretic connection 

 with the fact that capacity is more sensitive 

 to changes of slope than to those of discharge. 

 When discharge is constant the changes of 

 velocity are caused by changes of slope, and 

 the changes in capacity are those due to the 

 changes of slope. When slope is constant the 

 changes of velocity are caused by changes of 



