ADJUSTMENT OP OBSEBVATIONS. 



71 



Iii treating the data of Table 9, the assump- 

 tion was made that the note "several grains 

 moving" corresponds to competent slope; and 

 averages were found of the values of mean 

 velocity and depth. 1 These are: 



Grade (E) (F) (G) (H) 



Mean velocity (ft./sec.).. 1.10 1.52 2.14 2.83 

 Depth (foot) 0.020 0.092 0.108 0.218 



When the logarithms of these numbers are 

 plotted the positions fall well in line, and the 

 representative line gives (F^, indicating the 

 mean velocity corresponding to competent bed 

 velocity) 



M>:M - (18) 



Assuming again that bed velocity is propor- 

 tional to mean velocity, and again assuming 

 the validity of the Chezy formula, we obtain 

 from (18) 



<Se-*L -(19) 



The two values of the exponent of F 2 derived 

 from the experiments, namely, 0.44 and 

 0.50, are both larger than the deductive 

 value, 0.33, of equation (17), but the dispar- 

 ity is quite natural in view of the indefiniteness 

 of the data and the uncertainties of the assump- 

 tions. Collectively the values indicate an order 

 of magnitude. 



The influence of range of fineness on compe- 

 tent slope appears to be of the same nature as 

 its influence on a, though much less pronounced, 

 but the determinations of competent slope are 

 too indefinite to give the greatest value to the 

 comparison. It is significant, however, that 

 while the logarithmic plots for grade (E) and 

 width 1.00 and for three different discharges 

 (Table 7) all yield values of a less than 0.05 per 

 cent, the experiments on competent slope (Ta- 

 ble 9) record for one of the discharges "no 

 grains moving" with a slope of 0.21 per cent, 

 and for another "very few, if any, grams mov- 

 ing" with a slope of 0.33 per cent. The values 

 of a in this case fall far below those for the most 

 mobile components of the debris grade which 

 has the largest range of fineness. The general 

 facts appear to be that a varies decreasingly 



1 A few series of observations on competent velocity have been made 

 by others. They pertain chiefly to flume traction and are cited in 

 Chapter XII. Login, whose results are given in Chapter VII, used the 

 methods of stream traction but omitted to measure the sizes of materials 

 transported. 



with range of fineness, and that competent 

 slope is subject to a variation of the same kind, 

 which may or may not be of the same magni- 

 tude. 



The cause of this variation is not surely 

 known, but a plausible suggestion in regard to 

 it may be made. In the experiments with 

 mixtures of two or more grades it was found that 

 before the slope had been established, espe- 

 cially when low velocities were used, the cur- 

 rent tended to sort the debris, building deposits 

 with the coarser part and delivering the finer 

 material at the end of the trough. In experi- 

 ments with a single grade the same tendency 

 doubtless existed. It was in fact observed in. 

 connection with dunes and antidunes, which 

 sometimes showed a shading in color due to 

 partial sorting with respect to density, the 

 heavier particles being dark, the lighter pale. 

 As the differences of size within a grade were 

 not such as to appeal strongly to the eye, con- 

 siderable sorting with respect to size might 

 take place without attracting attention. With 

 the ordinary routine of the experiments, which 

 began in each series with low slopes and veloci- 

 ties and gradually increased them, the influ- 

 ences of such sorting may have been systematic, 

 and thus may have modified that relation of 

 values which finds expression in the constant a. 

 The result of such influence would be more pro- 

 nounced for grade (E) than for grades with 

 smaller range of fineness. It is easy to see also 

 that an allied influence may have affected to 

 some extent the interpretation of the experi- 

 ments on competent slope. 



The variations of a are paralleled in so many 

 ways by the variations of competent slope as 

 to leave little doubt that the one is in some 

 way representative of the other. It can not 

 be said that the constant a, arbitrarily intro- 

 duced to rectify curves and thereby facilitate 

 interpolation, is the equivalent of the slope of 

 competence if for no other reason than that 

 the competent slope for a grade of de'bris made 

 of unequal grains eludes precise definition 

 but it may well be a complex function of the 

 competent slopes of all the different sorts of 

 grams contained in one of the laboratory 

 grades. 



For the practical purpose of obtaining values 

 of a for use in formulas of interpolation, the 

 preceding discussion yields a large body of 

 pertinent information. Sigma varies inversely 



