RELATION OF CAPACITY TO FORM RATIO. 



127 



sions of figure 40. If the data were precise, 

 ami if equation (48) were strictly accurate, the 



300 



zoo 



100 



400 



300 



200 



100 



200 



100 



GracLe 



Grade 



Means 



S) 



C) 



\ 2 



FIGURE 40. Capacity for traction in relation to width of channel, when 

 depth and slope are constant. Scale of capacities, vertical; widths, 

 horizontal. 



oblique lines of the figure would all be straight 

 and would all intersect the line of zero capacity 

 somewhere to the right of the origin. The 



irregularities of the lines are of such distribution 

 as to indicate that they are occasioned chiefly 

 by the imperfection of the data, and so far as 

 may be judged by their inspection the formula 

 is substantially correct. 



As the individual lines do not well indicate 

 the points of intersection with the horizontal 

 axis, a set of composites were prepared, each 

 combining the data for a particular depth, 

 without distinction as to grade of debris or 

 slope of channel. In the computations for 

 these a few interpolations were first made, and 

 then the capacities were combined by taking 

 their geometric means. The numerical results 

 appear at the bottom of Table 24, and these 

 are represented by dots in the lower division of 

 figure 40. The indications of the dots were 

 then generalized by drawing straight lines 

 among them, and the intersections of these 

 lines with the line of zero capacity gave points 

 corresponding to D in figure 39. More strictly, 

 the distance of each intersection from the 

 origin gave an estimate of the quantity 2 DB 

 in equation (48). As each estimate is asso- 

 ciated with a particular depth, and as = -3 , 



the intersections give also values of the con- 

 stant oi in (49). 



As the plotted dots are so irregular as to 

 admit of much latitude in the drawing of the 

 lines, these values of the constant are far from 

 precise. No inference may be drawn from their 

 differences, and collectively they serve only to 

 indicate an order of magnitude. For fine sand, 

 with slopes of about 1 per cent, the constant 

 has a probable magnitude of 2 or 3. 



CAPACITY AND DEPTH. 



To consider separately the response of capac- 

 ity to variation of depth, the assumption of 

 constant discharge and variable width must 

 again be laid aside, and there must be substi- 

 tuted for it the assumption of constant width 

 and slope, with variable discharge. That is, 

 we are to conceive a stream of constant width, 

 of which the discharge and load are simultane- 



