156 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



the reentrants are doubtless stationary eddies, 

 with reversed currents where the value of V p is 

 negative. It appears equally difficult to give 

 definition to the bed as a datum from which to 

 measure upward, and to select and define a 

 locus for bed velocity. There is reason to sus- 

 pect also that the problem as thus stated is 

 unduly simplified by the assumption that the 

 bed is a stable entity, clearly separate from the 

 zone of saltation above. It did indeed so ap- 

 pear when the process of saltation was studied 

 through the glass wall of the observation 

 trough, but what was witnessed was the phase 

 of the process at the edge of the channel bed, 

 where the current was retarded by the resist- 

 ance of the channel wall. At a distance from 

 that wall, in the region where the cloud of sal- 

 tatory particles effectually precludes visual ob- 

 servation, the passage from stability to mobil- 

 ity may be less definite. I am led to this sug- 

 gestion by the observations, quoted byMcMath, 1 

 of a civil engineer who descended in a diving 

 bell to the bottom of the Mississippi at a point 

 where the depth was 65 feet and the bottom of 

 sand. Stepping to the bed, he sank into it 

 about 3 feet, and then thrusting his arm into the 

 yielding mass, could feel its flowing motion to a 

 depth of 2 feet, the velocity diminished down- 

 ward. In interpreting these phenomena, allow- 

 ance must be made for the fact that the pres- 

 ence of the diving bell created an abnormal 

 condition and if it rested on the bed put a stop 

 to saltation. The flow of the sand is then to be 

 ascribed to the difference in water pressure on 

 the two sides of the bell. But the fact of the 

 flow seems to indicate an antecedent state of 

 mobility, a laj'-cr of the bed being supersatu- 

 rated so as to have the properties of quicksand. 

 If such a layer exists, then the transition from 

 the bed to the saltation zone is not abrupt but 

 gradual. 



The difficulties in attempting to define bed 

 velocity are supplemented by those which affect 

 the measurement of velocities near the bed 

 while traction is in progress (p. 26), and to- 

 gether they have served to prevent the use of 

 bed velocity as a factor for quantitative com- 

 parison with capacity. This result has been 

 regretted because the forces which accomplish 

 traction are applied directly through the veloc- 

 ities of water near the bed, and it was admitted 



i McMath, R. E., Van Nostrand's Mag., vol. 20, p. 227, 1879. 



only after the failure of repeated attempts to 

 obtain serviceable estimates of bed velocity. 



In the present chapter observed or interpo- 

 lated capacities are compared with mean veloc- 

 ities of the stream, mean velocity being com- 

 puted as the quotient of measured discharge by 

 measured sectional area. The measurements of 

 discharge and width being relatively simple and 

 accurate, the determinations of mean velocity 

 have the same degree of precision as the meas- 

 urements of depth. (See p. 26.) 



In comparing capacity with mean velocity, 

 it is convenient always to treat fineness of 

 debris and width of channel as constants, but 

 it is also advantageous to recognize three 

 separate points of view as to the status of 

 discharge, slope, and depth. 



First, We may treat discharge as constant, 

 in which case slope and depth vary, along with 

 velocity and capacity. Each of the observa- 

 tional series (Tables 4, 12, and 14) conforms 

 to this viewpoint. When discharge is con- 

 stant, the increase of power necessary to 

 increase velocity is given by increase of slope, 

 and the increase of velocity causes the un- 

 changed discharge to occupy less space. As 

 velocity and capacity increase, slope increases 

 and depth decreases. 



Second, we may treat slope as constant. 

 With slope constant, the increase of power 

 necessary to increase velocity is given by 

 increase of discharge, but the rate at which 

 discharge is increased is greater than the rate 

 of increase given to velocity, and the increased 

 discharge therefore requires more space. As 

 velocity and capacity increase, both discharge 

 and depth also increase. 



Third, we may treat depth as constant. 

 To increase velocity by increasing slope will, 

 as we have seen, reduce depth. To increase 

 velocity by increasing discharge will, as we 

 have seen, increase depth. To increase velocity 

 without changing depth, it is necessary to 

 enlarge both slope and discharge. No experi- 

 ments were conducted with fixed depths, but 

 the data for this comparison are readily 

 obtained by interpolation. 



It is proposed to examine the relation of 

 capacity to velocity from each of these view- 

 points, developing the results so far as neces- 

 sary to give a basis for a comparison of the 

 viewpoints. 



