ADJUSTMENT OF OBSERVATIONS. 



89 



discovered a tendency toward parallelism, 

 within each group, of lines associated with a 

 particular sand grade and channel width but 

 differing as to discharge. For numerous other 

 groups, involving very irregular observational 

 positions, such parallelism was assumed; and 

 under that assumption the bettor series of a 

 group were made to control the directions of 

 the lines for the poorer. For three groups the 

 directions were interpolated by use of the 

 directions found in affiliated groups. 



For each observational series the direction 

 of the representative line gave the value of n^ 

 in equations (21) and (22), and the intersection 

 of the line with the axis of log d gave the value 

 of I'. 



TABLE 13. Value* ofn t in d^. 



In Table 13 the determinations of n t are 

 assembled, being arranged vertically with re- 

 spect to grade of d6bris and horizontally with 

 respect to width of trough. Collectively they 

 indicate that, for constant discharge, the depth 

 varies inversely with the slope and less rapidly 

 than the slope. Comparatively they indicate 

 considerable range in the rate of variation. 



TABLE 14. Adjusted values of depth of current (d), with values of mean velocity ( V m ) and form ratio ^R=J . 

 [i. Exponent in adjusting formula (21); p. e., probable error, in per cent, of adjusted values.] 



There is some suggestion of system in the dis- 

 tribution of values of n lt and it is especially 

 probable that to the coarser debris belong the 

 smaller values, but irregularity is, on the whole, 

 more in evidence than system. The irregu- 

 larity is to be ascribed largely to the imperfec- 

 tion of the data, and imperfection is believed 

 to inhere especially in the measurements of 

 depths by means of the gage. (See p. 25.) 



Table 14 contains series of adjusted or in- 

 terpolated values of depth. These were com- 

 puted for slopes with the constant interval of 

 0.2 per cent, the range of slope within each se- 

 ries being approximately the same as the range 

 through which the depth observations were 

 made. The range is usually less than the 

 range of slopes for which capacities were com- 

 puted, the difference being occasioned by the 

 fact that satisfactory measurements of depth 

 could not be made during vigorous antidune 

 traction. The computations were graphic, the 

 values of adjusted depth being read directly 

 from the logarithmic plot. 



The number of series represented in the table 

 is 73, being one-fourth less than the number for 

 which capacities and slopes were tabulated. 

 For 18 series the depth measurements were not 

 reduced, the chief reasons for rejections being 

 either (1) that the number of observations was 

 very small, (2) that the observations included 

 none made in connection with the smooth 

 phase of traction, and (3) that the measure- 

 ments with gage differed systematically by a 

 large amount from corresponding measure- 

 ments by the method of profiles. 



