236 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



laboratory formula is applicable. It is true 

 that fineness enters in a relatively complex 

 way into the determination of the loads of 

 natural streams, but for the comparison indi- 

 cated the elements of influence are severally 

 represented by the experiments, and their to- 

 tals should follow a law of the same type. For 

 small discharges this inference is subject to 

 certain qualifications, which will appear from 

 what follows. 



When the work of the same stream is com- 

 pared under different discharges, a difference in 

 fineness is developed under the laws of compe- 

 tence. With larger discharge the mean fine- 

 ness is less than with small discharge, and the 

 difference in fineness conspires with the differ- 

 ence in discharge to determine capacity. For 

 reasons explained in the last section, however, 

 capacity can not always be considered synony- 

 mous with load when the discharge is small. 



THE FORM-RATIO FACTOR. 



In the reaches of a direct alluvial stream there 

 is approximate uniformity of depth at high 

 stage, and the conditions involving form ratio 

 are essentially like those realized in the labora- 

 tory. To such cases the principles developed 

 in the laboratory studies should be applicable. 



It is true in a general way, as already men- 

 tioned on page 223, that at a high stage of a 

 natural stream the sectional area is about the 

 same for the reaches as for the bends, and so 

 too is the width. It follows that the mean 

 depth is about the same, although the maxi- 

 mum depth may be very different. The high- 

 stage capacity is also the same at every sec- 

 tion, after the channel form has been adjusted 

 to the discharge. If these generalizations are 

 correct, the principle involved in the form-ratio 

 factor of the laboratory formula is applicable to 

 curving streams, provided form ratio is inter- 

 preted as the ratio of mean depth to width, and 

 not as the ratio of maximum depth to width. 



In the analysis of conditions determining the 

 relation of capacity to form ratio (Chapter IV) 

 an important role was ascribed to the resistance 

 of the banks; and the quantity of that resist- 

 ance was represented in one of the parameters 

 of the formula, ot. The optimum form ratio, 

 p, was found to vary inversely with at and, there- 

 fore, to vary inversely with the resistance of the 

 banks. The resistance afforded by river banks 



is greater than that given by the smooth walls 

 of laboratory channels, and this element tends 

 to make the optimum form ratio relatively 

 small for rivers. Its influence, however, is over- 

 shadowed by those of slope and discharge. As 

 the optimim ratio varies inversely with slope, 

 and as most rivers have lower slopes than the 

 experimental streams, the general tendency of 

 the slope element is to make the ratio large 

 for rivers. As the optimum ratio varies in- 

 versely with discharge, and as the discharges of 

 natural streams are relatively large, the tend- 

 ency of this element is to make the ratio small 

 for natural streams. The rates of variation 

 being unknown, the net result of the three in- 

 fluences can not be inferred deductively. The 

 data from Yuba River, cited in Chapter IV (p. 

 135), show that for one case of a natural stream 

 the optimum ratio is decidedly larger than that 

 established by the stream in its alluvial phase 

 and is of the order of magnitude of the determi- 

 nations made in the laboratory. 



THE FOUR FACTORS COLLECTIVELY. 



The results of the preceding discussions ad- 

 mit of a certain amount of generalization. 

 When different streams of the same type are 

 compared, and especially when the type is al- 

 luvial, the law of their relative capacities at 

 high stage may be expressed by the laboratory 

 formula (109). The ability of that formula to 

 express the variation of capacity with discharge 

 in the same stream is problematic. 



It has not been shown that the system of 

 numerical parameters determined for laboratory 

 conditions can be used in extending the appli- 

 cation of the formula to natural streams. If 

 the formula were rational, the result of an ade- 

 quate mathematical treatment of the physical 

 principles involved, the constants measured in 

 the laboratory would be of universal application 

 (with moderate qualification for the conditions 

 imposed by the curvature of natural channels) ; 

 but the constants of an empiric formula afford 

 no basis for extensive extrapolation. 



THE HYPOTHESIS OF SIMILAR STREAMS. 



When the Berkeley experiments were planned 

 it was assumed that the relations of capacity to 

 various conditions would be found to be sim- 

 ple, and that the laboratory streams were rep- 

 resentative of natural streams except as to tie 



