THE OBSERVATIONS. 



31 



the bed again at D. The space overleaped 

 between C and D is occupied by one or more 

 slow-moving eddies. From A to C there is 

 traction, the material being derived from the 

 slope between A and B. At C the debris, 

 being abandoned by the current, is dumped, 

 and it slides by gravity down the slope CE. 

 So the upstream face of the wave is eroded and 

 the downstream face built out, with the result 

 that the wave, as a surface form, travels 

 downstream. As this is precisely what takes 

 place when a sand hill travels under the 

 influence of the wind, the name of the eolian 

 hill has been borrowed, and the waves are 

 called dunes. 1 In one of the narrower troughs 

 of the laboratory the dunes formed a single 

 line. In a wider trough their arrangement 

 sometimes suggested a double line, the crests 



of one being opposite the hollows of the other, 

 but their arrangement continually changed. 

 On the bed of a broad, shallow stream they are 

 apt to have a subregular imbricated pattern. 2 

 In a deep stream a single dune may be nearly 

 as broad as the channel. In the laboratory 

 the forms were inconstant, but the type was 

 about as broad as long, with the front edge 

 convex downstream. In natural streams the 

 dunes show great variety in outline, some being 

 described as longest in the direction of the 

 current and others as greatly extended in the 

 transverse direction. They vary in size with 

 the size of the stream, but especially with the 

 depth, and are transformed and remodeled 

 with increase and reduction of discharge. The 

 horizontal dimensions of most laboratory 

 examples may be conveniently described in 



J): 



FIGURE 10. Longitudinal section illustrating the dune mode of traction. 



inches, but river examples may require scores 

 or hundreds of feet. 3 The maximum height in 

 the laboratory was probably 2 inches; for 

 those in Sacramento River 2 feet has been 

 reported, and for those in the Mississippi 22 

 feet. 



In each series of laboratory experiments to 

 determine the relation of load to slope the 

 initial run was made with a small load, while 

 for the succeeding runs the load was pro- 

 gressively increased. Enlargement of the load 

 caused increase of slope and velocity, with 

 decrease of depth, and these changes were 

 accompanied by changes in the mode of trans- 

 portation. In the earlier runs dunes were 

 formed, and these marched slowly down the 

 trough. Then, somewhat abruptly, the dunes 

 ceased to appear, and for a number of runs the 



i This is the name chiefly used by Swiss investigators (see De Candolle, 

 Arch. sci. phys. et nat., vol. 9, p. 242, 1883, and Forel, idem, vol. 10, p. 43, 

 1884), and many observers compare the subaqueous feature to the eolian; 

 but the specific title commonly used in the United States and Great 

 Britain is sand wane, and some French engineers employ grbee. In the 

 present paper, dune is preferred to sand wave because there is occasion 

 to distinguish two species of debris waves. 



channel bed was without waves and approxi- 

 mately plane, although somewhat ruffled in the 

 run immediately following the disappearance of 

 dunes. Finally a third stage was reached in 

 which the bed was characterized by waves of 

 another type. These are called antidunes, 

 because they are contrasted with dunes in 

 their direction of movement; they travel 

 against the current instead of with it. Their 

 downstream slopes are eroded and their up- 

 stream slopes receive deposit. They travel 

 much faster than the dunes, and their profiles 

 are more symmetric. The water surface, 

 which shows only slight undulation in connec- 

 tion with dunes, follows the profiles of anti- 



* The imbricated pattern is frequently seen beneath tidal waters, 

 where ripple marks due to the reaction of wind waves are transformed 

 into dunes when the tidal current sweeps across them. It is then usually 

 to be ascribed to a difference in direction of the two actions. An elabo- 

 rate account of its development in rivers is given by H. Blasius, who has 

 recently investigated the whole subject of the rhythmic features of river 

 beds. See Zeitschr. Bauwesen, vol. 60, pp. 465-472, 1910. 



Arthur Hider, who studied dunes in the lower Mississippi, reported 

 a maximum length, crest to crest, of 750 feet, a maximum height of 22 

 feet, and a maximum progression of 81 feet in a day. See Mississippi 

 River Comm. Rept., 1882, pp. 83-88 (=Chief Eng. U. S. A., Kept., 1883, 

 pp. 2194-2199). 



