136 



TRANSPORTATION OF DEBBIS BY RUNNING WATER. 



0.06; and it is evident that the larger ratio is 

 much more efficient than the smaller. The 

 data do not serve to define the optimum form 

 ratio, but merely show that it is much greater 

 than 0.008. In this instance the slopes and 

 fineness are of the same order of magnitude as 

 those realized in the laboratory, but the dis- 

 charges are of a higher order. 



When water without detrital load is con- 

 veyed by an open rectangular conduit, the 

 form ratio of highest efficiency is that which 

 yields the highest mean velocity. It is ap- 

 proximately 1:2. This corresponds to the 

 maximum value of the optimum ratio for trac- 

 tion, and the correspondence might have been 

 expected on theoretic grounds. The two fac- 

 tors which, in ultimate analysis, determine 

 capacity for traction are velocity of current 

 along the bed and width of bed. When dis- 

 charge and slope are such as barely to afford 

 competence with the most favorable form 

 ratio, that ratio is one giving the highest 

 velocity, namely, 1:2. The other factor, 

 width of bed, is evidently favored by lower 

 values of R; and therefore, as the conditions 

 recede from the limit of competence, the opti- 

 mum form ratio becomes smaller. This line 

 of reasoning might, in fact, have been used to 

 show a priori what has actually been shown 

 by the experiments that the value of p varies 

 inversely with slope, discharge, and fineness. 



SUMMARY. 



Capacity for traction varies with the depth 

 of the current, being approximately (though 

 not precisely) proportional to a power of the 

 depth. Capacity varies also with the width 

 of the current, being approximately propor- 



tional to the width less a constant width. 

 This constant width is equivalent to the prod- 

 uct of the depth by a numerical constant. 

 When the discharge is constant, any change of 

 width causes a change of depth and also a 



change of form ratio, R = -. A formula for the 



variation of capacity in relation to form ratio, 

 when the discharge is constant, is based on the 

 above-mentioned properties and takes the 

 form 



C=l 2 (l-aR)R m ..(54) 



in which a is a numerical constant; or 



in which p is the optimum form ratio, or the 

 form ratio giving the highest capacity. 



That capacity should have a maximum value 

 corresponding to some particular value of form 

 ratio is made to appear from theoretic con- 

 siderations, and the fact of a maximum is 

 shown by the experimental data. The same 

 data show that the optimum form ratio has 

 different values under different conditions, its 

 values becoming smaller as slope, or discharge, 

 or fineness increases. 



The sensitiveness of capacity to the control 

 of form ratio is indicated in the formulas by 

 the exponent of R, and that also varies with 

 conditions. It becomes smaller as slope, or 

 discharge, or fineness increases. 



It is believed that all the generalizations 

 from the laboratory results may be applied to 

 natural streams, but only in a qualitative way; 

 the disparity of conditions is so great that the 

 numerical results can not be thus applied. 



