ADJUSTMENT OF OBSERVATIONS. 



59 



In the earlier experiments with contraction 

 at outfall as in other experiments it was 

 necessary to continue a run, with uniform 

 discharge and uniform feed of debris, until 

 the slope of the sand bed had been automat- 

 ically adjusted to the conditions. The criteria 

 adopted for recognition of a state of adjust- 

 ment were two that the water slope equal 

 the bed slope and that the rate of delivery 

 of debris equal the rate of feed. It was found 

 impracticable to satisfy these tests, because 

 both slopes and the rate of delivery fluctuated 

 through a wide range, and an approximate 

 adjustment, if attained, could not be made to 

 continue. The state of affairs may be likened 

 to the waving of a flag in the wind; at the 

 outer margin the amplitude of the undulation 

 is much greater than close to the staff. In 

 the long trough the outfall end corresponded 

 to the staff, giving a fixed position and ele- 

 ment of uniformity to which the profiles con- 

 formed, and the rhythmic departures were 

 greater with distance from the outfall. The 

 shorter trough when combined with 'end con- 

 traction represented a segment of the long 

 trough at a distance from the outfall and was 

 correspondingly subject to great fluctuations. 

 Despite these difficulties, the nature of which 

 was not well understood at the tune, a large 

 number of experiments were made in this way. 



The work with free outfall was affected 

 chiefly by terminal influences, and as these 

 produced systematic errors there was danger 

 of false conclusions. The work with con- 

 tracted outfall was affected by accidental 

 errors of such magnitude as largely to mask 

 the nature of the laws sought. Between 

 these perils of Scylla and Charybdis a middle 

 course was finally steered by using a moder- 

 ate amount of contraction, whereby the recog- 

 nized systematic errors were practically avoided 

 without the introduction of insuperable rhyth- 

 mic irregularities. 



SLOPES OF DEBRIS AND WATER SURFACE. 



The slope of the bed of debris to which 

 measurement was applied had been estab- 

 lished by the stream as that appropriate to 

 the stream's load of debris. It was caused 

 by the load, in conjunction with the discharge 

 and other conditions, and it accurately sufficed 

 to give the stream capacity for that load. 

 This was my point of view in arranging the 



experimental methods, and accordingly one of 

 the principal measurements undertaken was 

 that of the debris profile. But the slope more 

 generally considered in hydraulic studies is that 

 of the water surface. Head, the hydraulician's 

 ordinary measure for the determination of 

 power, is the vertical interval between two 

 points of the water surface, and slope is the 

 loss of head in a unit of distance. Under 

 conditions of uniform flow the two profiles 

 are parallel, but for various reasons our ex- 

 perimental currents ordinarily lacked so much 

 of uniformity that the two slopes were appre- 

 ciably different. I do not find it easy to 

 decide which slope should be regarded as the 

 true correlative of capacity for traction, but 

 as all our laboratory data include the debris 

 slope, while the determinations of water slope 

 were relatively infrequent, the discussion of 

 results has adhered almost exclusively to the 

 former. If the water slope is the true cor- 

 relative, then the use of the debris slope 

 involves a systematic error. 



THE LOGARITHMIC PLOTS. 



When the data of an observational series 

 are plotted on ordinary section paper, as in 

 figure 13, and a representative line is drawn 

 through or among them, that line is the graphic 

 equivalent of 



C=f(S) (2) 



When they are plotted on logarithmic section 

 paper, as in figure 14, and a representative 

 line is drawn, that line is the graphic equiva- 

 lent of 



.(3) 



The second equation, or line, is the logarith- 

 mic form of the first. 



As already mentioned, a logarithmic plot 

 was made of each observational series. The 

 plot included primarily the slopes of the de- 

 bris bed and the determinations of load from 

 the delivery of debris at the end of the trough, 

 but it included also, with distinctive nota- 

 tion, such determinations as were available 

 of water-surface slopes and of load based on 

 the rate of feed at the head of the trough. 

 The notation also classified observations with 

 reference to the three modes of traction and 



