368 S. H. BARRACLOUGH AND T. P. STRICKLAND. 
-2° F. or approximately ‘1° C., and it is thought that the tempera- 
tures as given in the tables may be relied upon to ‘2° C. 
11. Relation between slope and velocity.—Two series of experi- 
ments (1. and II.) were made with nominal values of the mean 
hydraulic radius of respectively 1:5 cm. and 1 cm., and witha 
wide range of slopes, in order to determine the method of variation 
of velocity with slope. As Series II. is the more complete and 
extensive of the two, it will be considered first. The following 
table summarizes the essential quantities. The velocities as given 
Table V. 
Series IJ.—Mean hydraulic radius=1:00 cm. Mean temp- 
ature = 16-2° C. : 
a e eli. as — oe ae ae 
7 48°2 16830 | ‘0071 38513 | #, F 
4 64°5 1°8096 | :0137 21367 | D, #,F 
5 731 1°8639 | -0176 22465 | 5 9 9 
B 81:2 1:9096 | -0221 | 23444 | Interpolated 
3 81:7 1°9122 | -0235 23711 | E, 
1 91:2 1:9600 | -0274 243878 | D, EF 
6 105°2 2°0220 | 0380 | 2:5798 | s » » 
2 1233 20910 | -0505 2°7088 | 9 1 » 
ll 1345 2°1287 | -0646 28102 | BE, F 
A 135°7 21326 | -0663 2°8215 | Interpolated 
In the al tab]. peri ts Band A interploted from Series B and 
Arespectively. . 
in the second column have been reduced to a common hydraulic 
radius. by the formula obtained in § 12, and to a common mean 
temperature by the formula obtained in§ 13, In Fig. 3, curve 
“II” in the lower half of the diagram shows the method of vari- 
ation of velocity with slope under the conditions obtaining in 
Series I]., and its logarithmic homologue is shown by the curve 
marked “II” in the upper half of the diagram. From the fact 
that there is a linear relationship between the logarithims of the 
slope and of the velocity it is at once evident that the function 
connecting these two quantities is exponential in form. — The 
inclination of the straight line is approximately °46, so that if... 
