RELATION OF CAPACITY TO VELOCITY. 



163 



complicated, for the present at least, for full 

 deductive treatment, and there are no adequate 

 experimental data. 



Most of the earlier experiments on compe- 

 tence pertained to flume traction, but it is 

 probable that in those of T. Login (1857) the 

 conditions were such as to give stream traction. 

 The currents he employed were shallow, and he 

 measured velocities by means of floats which 

 occupied half the depth of the water. 1 As 

 dimensions of transported particles are not 

 included in his report of observations, a numer- 

 ical formula can not be based on it. 



Experimental data on competent velocity for stream traction. 



[By T. Login.] 



Velocity 

 in ft. /sec. 



Brick clay, mixed with water and then allowed to 

 settle ......................................... 0. 25 



Fresh-water sand .................................. 67 



Sea sand ......................................... 1.10 



Rounded pebbles, size of peas .................... 2. 00 



John S. Owens, experimenting on the trans- 

 porting power of sea currents, made use of 

 small streams flowing from one tide pool to 

 another. Measuring velocities by means of 

 floats, he tested the ability of currents to move 

 pebbles, 0.5 inch to 6 inches in diameter, over 

 a channel bed of sand. 2 His results are formu- 

 lated in 



45 



where D l is diameter of pebble in inches, V 

 velocity in ft./sec., and TPthe weight in pounds 

 of a cubic foot of the material of the pebble. 

 This is equivalent to 



.(82) 



0.059 

 J 'G-1 ' 



where D is the diameter in feet and G the den- 

 sity of the material. 3 



Of the Berkeley experiments on compe- 

 tence, recorded in Tables 9 and 10, a single 

 series bears on the point under consideration, 

 but its bearing is less diiect than could bo 



' Royal Soc. PMinburgh Proc., vol. 3, p. 475, 1857. 



2 Geog. Jour., vol. 31, pp. 415-420, 1908. 



See also experiments by T. E. Blackwell, cited in Chapter XII. 



desired. By selecting from Table 9 data cor- 

 responding to a trough width of 1 foot and a 

 discharge of 0.363 ft. 3 /sec. I was able to make a 

 logarithmic plot of diameters of particles of 

 grades (B), (C), (D), (E), (G) in relation to 

 competent mean velocities, and this plot gave 

 the following equation: 



-0.0025 



F m "....(83) 



The exponent 2.7 is connected with the fact 

 that V m in this case is mean velocity with dis- 

 charge constant. It is easy to infer from the 

 data assembled in Table 53 that if either depth 

 or slope had been the constant condition in the 

 experiments a smaller exponent would be in- 

 dicated. So the possibility remains that the 

 Leslie law is true of mean velocities provided 

 the depths increase along with the velocities, 

 and the experimental data manifestly do not 

 apply to bed velocities. 



In order to compare the Berkeley observa- 

 tions with Login's, the diametera of his mate- 

 rials have been computed by equation (83). 

 The diameter found for brick clay, 0.00006 foot, 

 is much too large; but this result is readily 

 accounted for by the fact that adhesion is an 

 important factor in the resistance of clay to 

 the action of the current. If the computed 

 diameters for his "fresh-water sand," 0.00085 

 foot, and "sea sand," 0.0032 foot, are correct, 

 those materials correspond severally to our 

 grades (A) and (D), a very fine sand and a 

 coarse sand. The diameter found for "peb- 

 bles, size of peas," is 0.016 foot, or one-fifth of 

 an inch. 



The coefficient obtained by Owens, 0.059 in 

 equation (82), is 14 times as large as our coeffi- 

 cient, 0.0042 in equation (83), a contrast 

 which accords in a general way with the differ- 

 ence between the classes of phenomena ob- 

 served. The pebbles he tested were rolled 

 over a bed of relatively fine material, which 

 gave them a smooth pathway with little resist- 

 ance, while the grains to be moved in our 

 experiments rested among similar grains and 

 were less readily dislodged. 



