ADJUSTMENT OF OBSERVATIONS. 



65 



comparing their logarithmic graphs. In figure 

 22 the curved line AB has been copied from the 

 curve in figure 19. It is the graph of log C= 

 f (log S) for grade (G), width 0.66 foot, and dis- 

 charge 0.734 ft.'/sec. If for S we substitute 

 S 0.3, we modify the graph by moving each 

 point of it to the left by an amount equal to 

 log S log (S 0.3); and we produce the lino 

 CD, which is the graph of log C=f a (\og 

 (S 0.3)). If in similar manner we derive 

 the graph of log C=f m (\og (S-0.6)), the re- 

 sult is the line EF. CD curves in the same 

 direction as AB but less strongly; EF curves 

 in the opposite direction. It is evident that 



the three curves belong to a continuous series, 

 and that somewhere between CD and EF a 

 member of the series is straight or approxi- 

 mately straight. That straight line, GH, is 

 the graph of log C=f IV Qog (5-0.39)); but as 

 it is straight, its equation may be written 



log <7=log 6, + n-log GS-0.39), 



in which log 6 t is the ordinate of the inter- 

 section of the line with the axis of log C, and n 

 is the trigonometric tangent measuring the 

 inclination of the line to the axis of log S. 

 This is identical with equation (15) except 

 that 0.39 appears in place of a; and in fact 



200 



100 

 80 



00 



20 



7 



.4 



Slop* 



.8 1.0 



Z.Q 



FIGCBE 22. The relation of in C=f(S-r) to the curvature of the logarithmic graph. 



the value of a in equation (lOa) was computed 

 graphically by means of the logarithmic plot. 



The line AB, being the graph of log C 

 /.Gog S), is also the logarithmic graph of 

 C=f(S). The line GE, being the graph of 

 log C^/jvGog (8 a)) is also the logarithmic 

 graph of <7=/ v (S a). Their relation in re- 

 spect to simplicity is that of the curve to the 

 straight line. 



In view of these suggestions of harmony it is 

 peculiarly pertinent to inquire whether a is 

 actually representative of competent slope: 

 and it will be convenient to make that inquiry 

 in connection with the determination of values 



20921 No. 8614 5 



of a for the several series of observations on 

 capacity and slope. 



THE CONSTANT a AND COMPETENT SLOPE. 



In the experimental data for graded debris 

 Table 4, (A) to (H) are 117 series of values 

 of capacity and slope. After these had been 

 plotted and inspected in a comparative way, 

 it was decided to restrict the main discussions 

 to 92 series only, the discarded series being all 

 short as well as somewhat discrepant among 

 themselves. Of the 92 series retained, only 

 30 afford information as to the correspond- 

 ing values of o; that is, only 30 of the loga- 



