28 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



sensible uniformity of process over the whole 

 width of channel are not consistent with the 

 idea that the saltation zone is invaded by 

 eddies of large dimensions, such as would bo 

 competent to sustain the grains by the up- 

 ward components of their motions. If there 

 were large ascending and descending strands 

 of current the visible surface of the zone 

 would be locally raised and depressed by 

 them. We must, indeed, assume that the flow 

 is turbulent, in the technical sense, because 

 parallel or laminar flow is impossible with 



FIGURE 6. The beginning of a leap, in saltation. 



velocities competent for traction, but the ed- 

 dies may be assumed to be of small dimen- 

 sions in relation to the depth of the zone, and 

 the lines of flow with which saltation is con- 

 cerned may be assumed to be approximately 

 parallel to the general direction of the current. 



The explanation I would substitute for that 

 of the uplift of grains by rising strands is that 

 each gram is projected from the bed with an 

 initial velocity which gives it a trajectory an- 

 alogous to that of a cannon ball. The follow- 

 ing fuller statement, though given with little 

 qualification, should be understood as largely 

 hypothetic. 



In figure 6 the current is supposed to move 

 from left to right above the grains of debris 

 shown in outline. A grain which in A is at 

 rest appears in B in an advanced position, 

 having been rolled upward and forward about 

 an undisturbed grain which lies in its way. 

 (The moving grain is doubtless more likely to 

 roll against two other grains than a single one, 

 but the principle is the same.) In moving to 

 its new position the center of gravity of the 

 gram describes a curve convex upward. The 

 grain continuously gains in velocity, and the 

 acceleration also increases as the direction of 

 motion comes to make a smaller angle with 

 the direction of the current. At each instant 

 the accelerative force due to the current and 

 that of gravity are combined and have a re- 

 sultant direction; and the combined or re- 

 sultant accelerative force may be resolved into 

 two parts, one of which coincides in direction 



with the motion of the center of gravity and 

 the other with the line joining the center of 

 gravity and the point of contact. The last- 

 mentioned component presses the moving 

 gram against the stationary grain. Opposed 

 to it is the centrifugal force arising from the 

 curvature of the grain's path; and the point 

 is finally reached where the centrifugal force 

 dominates and the grain is free. Under the 

 ordinary conditions of saltation this point is 

 not the crest of the obstruction, but is on the 

 upstream side, so that the grain's direction of 

 motion at the instant of separation is obliquely 

 upward. Thus the free grain is initially mov- 

 ing upward as well as forward, and it has al- 

 most literally made a leap from the bed. 



If the grain were at that instant released 

 from all influences but gravity, its path before 

 returning to the bed would be the arc of a 

 quadric parabola with vertical axis. The 

 actual deviation of its trajectory from the 

 parabolic form is analogous to that observed 

 in gunnery, for it arises from the resistance of 

 a fluid; but the laws of resistance are not the 

 same for air and water, and the frictional ac- 

 celeration in one case is negative while in the 

 other it is mainly positive. The trajectory in 

 gunnery is shorter than the ideal parabolic 

 arc; in saltation it is longer. 



Figure 8 gives diagrammatically the trajec- 

 tory of a saltatory grain. In figure 7 AB 

 is a portion of the same trajectory. Let the 

 space AC represent the instantaneous velocity 

 of the grain, and let the line AD represent in 

 direction and length the velocity of the water 



FIGURE 7. Diagram of accelerations affecting a saltatory grain. 



about the grain. Then, C and D being con- 

 nected by a line, CD represents in direction 

 and magnitude the relative velocity of water 

 and grain, or the velocity of the water as re- 

 ferred to the grain. By reason of the mutual 

 resistance of water and grain, this relative mo- 

 tion accelerates the grain, the acceleration be- 

 ing a function of the differential velocity, the 

 size of the grain, and other conditions. On the 

 line CD, showing the direction of the accelera- 

 tion, let the space CE represent its amount. 

 Then from E draw the vertical EF, represent- 



