PEOBLEMS ASSOCIATED WITH RHYTHM. 



243 



interval was determined by a preexistent water 

 rhythm. Xot only was the dune interval a 

 function of depth and velocity of current, 1 but 

 the creation of dunes by water rhythm was 

 repeatedly observed. In certain experiments a 

 slow current, moving over a bed of debris arti- 

 ficially smoothed and leveled, was gradually 

 quickened until transportation began. The 

 movement of particles did not begin at the same 

 time all along the bed but was initiated in a 

 series of spots separated by uniform intervals, 

 and the first result of the transportation was the 

 creation of a system of dunes. 



In certain experiments on flume traction a 

 slow current, moving over a smooth channel 

 bed of wood, swept along a small quantity of 

 sand. With increase of the load of sand local 

 deposits were induced, which took the form of 

 thin straggling patches, similar to one another 

 in outline and separated by approximately 

 equal bare spaces. These moved slowly down- 

 stream, the mode of progress being similar to 

 that of dunes, and with further increase of load 

 they acquired the typical profile of dunes. 



In both groups of experiments it was evident 

 that the primary rhythm pertained to the water 

 and was independent of the work of transpor- 

 tation. In the second group, where sand swept 

 steadily forward over the whole area of the bed, 

 it was evident that the water rhythm did not 

 involve reversed currents along the bed and 

 therefore did not include such stationary vor- 

 tices as accompany dunes. 



In the experiments on stream traction the 

 development of dunes was conditioned by the 

 three factors of velocity, depth, and load, be- 

 sides an undetermined influence from fineness 



i Measurements of dune interval in the laboratory were too few to dem- 

 onstrate the factors of control, but comparison of laboratory data with 

 data from other sources leaves little question that control is exercised by 

 depth, velocity, and fineness. In the laboratory, where depths were a 

 matter of inches, the dune interval rarely exceeded 2 feet. In Mississippi 

 River depths measured in scores of feet are associated with intervals 

 measured in hundreds of feet. In tidal estuaries, where dunes of a 

 special type are exposed at low tide, the depths of the formative cur- 

 rents are intermediate between those of the laboratory and those of the 

 Mississippi, while the intervals are measured in feet or tens of feet. For 

 data of the Mississippi see Johnson, J. B., Kept. Chief Eng. U. 8. A., 

 1879, pp. 1963-1967, and Eng. News, 1885, pp. 68-71; Powless, W. H., 

 Mississippi River Comm. Kept, for 1881, pp. 66-120; and especially 

 Hider, Arthur, Mississippi River Comm. Rept. for 1882, pp. 83-88. For 

 data on the dunes of tidal estuaries see Cornish, Vaughan, Geog. Jour., 

 vol. 18, pp. 170-202, 1901. Hider finds that the dune interval is greater 

 at high stages of the river than at low, the depth and velocity both 

 decreasing with the change from high to low. Cornish's observations 

 show that the interval varies directly with depth of current under condi- 

 tions which make it probable that the velocity varies inversely with 

 depth. 



of debris. 2 It is probable that load and fine- 

 ness enter only as factors of resistance, so that 

 the essential conditions are velocity, depth, and 

 bed resistance. Within certain rather wide 

 ranges of value for these controlling factors the 

 bed is molded into dunes. When the limit is 

 exceeded by increase of velocity or resistance, 

 or by decrease of depth, the dunes disappear 

 and the bed becomes smooth and plane. At 

 the same time the oscillations and other dis- 

 turbances of the water surface are reduced; but 

 as they do not altogether disappear it is to be 

 inferred that the flow is still characterized by 

 internal diversity. 



With still further increase of velocity or 

 resistance, or with further reduction of depth, 

 another critical point is passed, and the process 

 of traction becomes again rhythmic, but in an 

 antithetic way. The bed is molded into anti- 

 dunes, which travel upstream (pp. 31-34), 

 and the water surface also is molded into 

 waves, which copy the forms of the antidunes 

 and move with them. The internal move- 

 ment of the water is again characterized by a 

 dominant rhythm, but the type of rhythm is 

 different from that associated with dunes. 

 The rhythm is also less stable, and its intensity 

 exhibits a cycle of change. With low intensity 

 the waves are nearly equal in height and 

 length, but sooner or later inequalities develop 

 and the higher waves overtake the lower and 

 absorb them. This process increases the wave 

 length in the upstream part of the trough, and 

 the influence of the change is hi some way 

 communicated to the downstream end, where 

 the waves are first formed, with the result 

 that larger and larger waves develop. Finally 

 a master wave, with curling crest, rushes 

 through the trough from end to end, and this 

 has the effect of wiping out the irregularities 

 and restoring the status of low intensity. 

 Various phases of the cycle are illustrated by 

 the profiles in figure 12 (p. 33). 



When combinations of velocity, resistance, 

 and depth similar to those causing antidunes 

 are made for a stream flowing through a rigid 

 straight channel, without movable debris, the 

 water develops surface waves, and these travel 



2 Eger, Dix, and Seifert (Zeitschr. Bauwesen, vol. 56, pp. 325-328) 

 found that under certain conditions dunes were developed in a sand of 

 uniform grade but not in a finer sand composed of several grades. In 

 our experiments the smooth phase of transportation had greater range 

 with mixed grades than with single grades. 



