THE OBSERVATIONS. 



33 



the width was 1.32 feet three sets formed. As the critical 

 velocity at which dune motion ceases is approached these 

 waves begin todisappear, and when thisvelocity is reached 

 the water surface is waveless. This waveless condition 

 continues as the rate of feed increases until sand motion 

 in antidunes begins, when large waves, the width of the 

 trough and corresponding in length to the sand waves 

 beneath them, are formed as illustrated in figure 11. 



In order to show the magnitude of these surface waves, 

 wave traces have been drawn. Some of these are given 

 in figure 12. A sheet of galvanized iron 4 feet long and 1 

 foot high was divided into inch squares by lines. This 

 plate was moistened and covered with fine dust. It was 

 held vertical at a given place over the experiment trough 

 and on signal was dropped into the trough and taken out 

 again as quickly as possible. The dust was removed from 

 that part of the plate in the water, leaving a well-defined 

 outline of the wave. This wave trace was quickly sketched 

 on paper by means of the lines marking the squares. Trace 

 A, figure 12, is for zero feed ; B is for a very small feed ; C is 

 for a larger feed, the surface being covered with the canoe- 

 shaped waves ; D shows one of the larger waves associated 

 with autidunes. 



The slopes at which the phases of traction 

 change are lower for large streams than for 

 small, and lower for fine debris than for coarse. 

 The phase with smooth bed which may con- 

 veniently be called the smooth phase covers 

 a greater range of conditions with mixed 

 debris than, with assorted. 



The processes associated with dunes and 

 antidunes were briefly studied in the glazed 

 trough and with the moving field. Trans- 

 portation by saltation follows the entire pro- 

 file of the antidunes but traverses the dunes 

 only from A to C of figure 10. The velocity 

 of saltatory grains is greatest where erosion 

 takes place, namely, along the upstream slopes 

 of dunes and the downstream slopes of anti- 

 dunes, and it may reasonably be inferred that 

 the water velocities are greatest in those 

 places. The eye detected no difference in water 



21 2Z 23 



FIGURE 12. Profiles of water surface, automatically recorded, showing undulations associated with the antidune mode of traction. Numbers 



show distance, in feet, from the head of experiment trough. 



depth over the two slopes of the antidune, and 

 if the depth is the same so also is the mean 

 velocity; but the ratio of bed velocity to mean 

 velocity is known to vary with conditions. 



The cause of the changes in process has not 

 been adequately investigated, but a few sug- 

 gestions may be made. To assist in a search 

 for controlling conditions, the factors con- 

 nected with the two critical points the change 

 from dune phase to smooth and the change 

 from smooth to antidune were tabulated 

 from the experiments with sand of a single 

 grade (C) ; the positions of the critical points 



being estimated by Mr. Murphy at a time when 

 the details of the experiments were freshly in 

 mind. In Table 3 w is the width of trough, in 

 feet ; Q the discharge, in cubic feet per second ; 

 8 the per cent of slope; d the depth of water in 

 feet; V m the mean velocity, in feet per second; 

 L the load, in grams per second; and L l the 

 load per unit width. The data in this table 

 are taken from a preliminary reduction of the 

 observations and are less accurate than the 

 results of the final adjustment, which appear 

 in Table 12 (p. 75). They suffice, however, 

 for the present purpose. 



TABLK 3. Data connected with changes in mode of transportation. 



20021 No. 80 14- 



