FLUME TRACTION. 



217 



the most economical discharge is sensibly pro- 

 portional to the width, so that for each slope 

 and grade of material there is a particular dis- 

 charge per unit of width giving a maximum 

 duty; and (3) that the most economical dis- 

 charge is greater for low slopes than for high. 



The first of these results is in fair accord with 

 our own. Five of the nine values of the expo- 

 nent o in Table 72 are loss than unity. For 

 the corresponding series the values of i a range 

 both below and above unity and the corre- 

 sponding values of the variable exponent for 

 duty in relation to discharge, i 3 1, range below 

 and above zero. The value zero evidently cor- 

 responds to a maximum value of duty. His 

 third result is in strict accordance with ours; 

 his second can not be compared without fuller 

 details. 



A diagram exhibiting his determinations for 

 the traction of crushed quartz sized by 40-mesh 

 and 150-mesh sieves shows for different dis- 

 charges per unit width the variation of duty 

 with slope. For the larger discharges duty 

 varies as the first power of slope ; for the small- 

 est discharge with the second power. This cor- 

 responds to a variation of capacity with the 

 second to third power of slope. Our most 

 available data for comparison are those of 

 grade (C), the capacity for which varies with 

 the 1.66 power of slope (Table 70). As grade 

 (C) was separated by 30-mesh and 40-mesh 

 sieves, it is considerably coarser than the 

 crushed quartz, and, being stream worn, it is 

 less angular. The marked difference in the 

 observed laws of variation is evidently suscepti- 

 ble of more than one interpretation, but it is 

 thought to be connected with difference in 

 fineness, as more fully stated on a following 

 page. 



F. K. Blue l made a series of experiments in 

 which the trough was of sheet iron, 50 feet long, 

 5 inches deep, and 4 inches wide, the bottom 

 being semicylindric with 2-inch radius. It was 

 so mounted that it could be set to any slope 

 up to 12 per cent. Two materials were used 

 as load, the first a beach sand of 60-mesh aver- 

 age fineness, the other a sharp quartz sand of 

 about 80-mesh fineness, containing about 10 

 per cent of slime from a stamp mill. With each 

 material the discharge and load were varied; 

 and for each combination of discharge and load 



i Eng. and Min. Jour., vol. 84, pp. 530-539, 1907. 



the slope was adjusted to competence, and 

 mean velocity was determined by means of a 

 measurement of depth. Discharge and load 

 were not measured directly but in certain com- 

 binations. Instead of discharge, the total vol- 

 ume of water and load was measured. This 

 quantity was used chiefly in the computation 

 of mean velocity, for which purpose it is better 

 fitted than is discharge alone. Load was meas- 

 ured as a volume, the volume of the transported 

 material as collected in a settling tank, and is 

 reported only through a ratio, q, which is the 

 quotient of the volume of load by the volume 

 of discharge plus load. This is essentially a 



duty but differs materially from duty ( U= . J 



as defined in the present report. Representing 

 by W the weight in grams of a cubic foot of 

 debris, including voids, and by v the percentage 

 of voids, it follows from the definitions that 



U qW 



2= w + m=v)' and = 1-gd-t;) 



From the discussion of his data Blue finds 

 (1) that q varies as the square of the slope 

 and (2) that it varies as the sixth power of the 

 mean velocity. He does not specifically con- 

 sider the relation of q to discharge, but exami- 

 nation of his tabulated data shows that q is 

 but slightly sensitive to variations of discharge 

 plus load. 



As Blue's coarsest material, the beach sand, 

 has approximately the fineness of our grade (A), 

 while the finest we treated in flume traction is 

 of grade (C), the most definite comparison of 

 results can not be made, but there is neverthe- 

 less interest in such comparison as is possible. 

 Computing values of 7 from his data for beach 

 sand, and plotting them in relation to slope, I 

 obtained UxS 2 - 02 This gives for capacity and 

 slope, C<xS 3M ; and the exponent 3.02 may be 

 compared with values of 7 t in Table 70, for the 

 smoothest kind of trough bed. The exponent 

 for grade (C) is 1.66, and the exponent has a 

 minimum value of 1.30 for grade (G). In 

 accordance with the generalization (p. 208) that 

 the sensitiveness of capacity to slope increases 

 from a minimum toward both coarse grades and 

 fine, we should expect for grade (A) an index 

 of sensitiveness materially greater than 1.66. 

 The data furnished by Blue thus tend to sup- 

 port the generalization, and additional support 



