PROBLEMS ASSOCIATED WITH BHYTHM. 



247 



0.66 foot; discharge, 0.545 ft. 3 /sec.; grade of 

 debris, (C). The variables are as follows: 



Load gm./sec 38 53 194 



Slope of bed... per cent.. 0.38 0.5G 1.14 



Depth at 17 feet from out- 

 fall feet.. 0.353 0.313 0.303 0.226 



Mean velocity... ft. /sec.. 2.57 2.64 2.73 3. 6G 



Level of maximum veloc- 

 ity; measured from the 

 surface as a fraction of 

 depth 0.7 0.1 



Letter indicating curve in 

 figure82 IB C D 



With the slope of 0.38 per cent the sand moved 

 in dunes; with 0.56 per cent the phase of trac- 

 tion was transitional between the dune and the 

 smooth; with 1.14 it was transitional between 

 the smooth and the antidune. The conspicu- 

 ous change associated with the addition of load 

 is the raising of the level of maximum velocity, 

 and this is correlated also with increase of slope, 

 increase of mean velocity, decrease of depth, 

 and modification of the mode of traction. 



The plotted points for velocities near the 

 channel bed are irregular when the observations 

 were made above a bed of loose debris, and 

 little use has been made of them in drawing the 

 curves. As previously mentioned, the presence 

 of the gage caused a deflection of the lines of 

 flow and the formation of a hollow in the bed. 

 Not only was it impossible to observe with 

 accuracy the relation of the instrument to the 

 normal position of the bed, but the velocity 

 observed was higher than that normally asso- 

 ciated with the depth at which the instrument 

 was placed. (See Appendix A.) 



In most of the groups of curves the variations 

 of form are associated with simultaneous varia- 

 tions of so many conditions that the nature of 

 the control is not evident. For satisfactory 

 interpretation a fuller series of observations 

 seems to be required, but certain inferences may 

 be drawn from those before us. 



Many of the peculiarities of form are con- 

 nected with the position of the level of maximum 

 velocity. The movements of the maximum in 

 relation to depth of current are of two kinds. It 

 rises with increase of depth when that increase 

 is caused by increase of discharge (fig. 79). It 

 falls with increase of depth when that increase is 

 independent of discharge (figs. 78, 81, and 82). 

 Apparently depth, considered by itself, is not 

 a factor of control. The maximum rises with 

 increase of mean velocity when that increase is 



due to increase of discharge (fig. 79), or of 

 slope (fig. 78), but falls with increase of mean 

 velocity when the increase is due to lessened 

 resistance of the channel bed (figs. 73, 80, 81, 

 and 82). Apparently mean velocity, consid- 

 ered by itself, is not a factor of control. If we 

 give attention to the three factors on which 

 depth and mean velocity chiefly depend 

 namely, discharge, slope, and bed resistance 

 a more consistent relation is found. Variations 

 of discharge affect only the group of curves in 

 figure 79, and there the maximum rises with 

 increase of discharge. Slope affects the groups 

 in figures 78, 81, and 82, and in each case the 

 maximum rises with increase of slope. Bed 

 resistance affects the groups in figures 80, 81, 

 and 82, and in each case the maximum rises 

 with increase of resistance. 



The lowering of the level of maximum veloc- 

 ity as the point of outfall is approached (fig. 73) 

 is a harmonious feature, but in that case there 

 is substituted for progressive reduction of bed 

 resistance an abrupt cessation of all channel 

 resistance. The resulting acceleration is propa- 

 gated upstream, and its amount has a vertical 

 distribution connected with pressure. In the 

 case of contracted outfall (fig. 74), there is 

 added an effect of convergence, which still fur^ 

 ther illustrates the graduation of acceleration 

 in relation to pressure. The influence of con- 

 traction is important in other connections, but 

 need not be further discussed in this place. 



The influence of outfall may extend to a 

 considerable number of the curves here figured. 

 In most of the experiments made without 

 contraction at outfall there was progressive 

 decrease of depth and increase of mean 

 velocity, from some point near the head of the 

 trough to its end. This was most marked 

 when the bed of the trough was horizontal 

 (figs. 73, 78-4, 79, 81-4, and 82-4). Reasoning 

 from the observed fact that acceleration in- 

 creases with depth, I think it probable that 

 under such conditions the level of maximum 

 velocity lies lower than it would with a uniform 

 mean velocity. 



Returning to the consideration of discharge, 

 slope, and resistance, we may note that the 

 variable resistance with which variations of 

 the curve have been definitely correlated is bed 

 resistance. In all the experiments the channel 

 sides had the same texture, so that the side 

 resistance was approximately proportional to 



