CHAPTER II. ADJUSTMENT OF OBSERVATIONS. 



OBSERVATIONS ON CAPACITY AND SLOPE. 



THE OBSERVATIONAL SERIES. 



Each of the experiments in stream traction 

 involved six quantities (1) a fineness, or 

 grade of d6bris, (2) a width of trough, (3) a 

 discharge, (4) a slope, (5) a load, or capacity, 

 and (G) a depth of current. The experiments 

 were arranged in series, for each of which grade, 

 width, and discharge were constant, while 

 within each the magnitudes of slope, capacity, 

 and depth were varied. There will be frequent 

 occasion to mention these secondary units of 



the experimental work, and whenever the title 

 series seems not sufficiently specific they will be 

 called observational series. The number of 

 such series recorded in Table 4 is 153. 



The factors of grade, width, and discharge, 

 which are related to an individual series as 

 fixed conditions, or constants, do in fact assume 

 the character of variables when series is com- 

 pared with series; but their modes of determi- 

 nation and combination are not of such char- 

 acter that their numerical values can be 

 checked and adjusted by means of recorded 

 relations. 



300 



Jzoo 



(0 



a. 

 1) 

 o 



100 









I 2 



Slope 



FIGURE 13. Plot of a single series of observations on capacity and slope. Capacity ingramsofdebrispersecond. Slope in percent. Themodesof 



traction are indicated. 



In each experiment the values of slope, load, 

 and depth are mutually dependent ; within each 

 series they form a triple progression, the depth 

 decreasing while slope and load increase; 

 but the laws of these interdependent varia- 

 tions are partly masked by irregularities in the 

 sequences. As a preliminary to the general 

 discussion, the observational values were sub- 

 jected to a process of adjustment, whereby the 

 sequences were freed from irregularities. The 

 irregularities are made manifest by the com- 

 parison of the sequences of two variables, and 

 first consideration will be given to those of 

 capacity and slope. 



Figure 13 exhibits the relations of capacity 

 to slope as observed in a single series of experi- 



ments (that for grade (C), with w=l.32 feet 

 and Q = 0.363 ft. 3 /sec.). The ordinates indicate 

 capacity, as measured by debris delivered 

 at the lower end of the trough; the abscissas 

 represent slope, as measured on the bed of 

 the channel. The arrangement of the observa- 

 tional dots suggests that if the observations 

 were harmonious the dots would fall in a 

 line of simple curvature. Such a line would 

 express the law connecting capacity and slope. 

 The departures of the dots from such linear 

 arrangement represent irregularities, or errors, 

 in the experimental data. The adjustment 

 proposed is the replacement of the imperfectly 

 alined dots by a generalized or representative 

 line, or the replacement of the inharmonious 



55 



