372 S. H. BARRACLOUGH AND T. P. STRICKLAND. 
Since, however, the results obtained in Series II. are, as has been 
shown, more reliable than those of Series I., and since if curve “I” 
were drawn parallel to curve “II” it would represent the plotted 
results almost as accurately as in its present position, it will | 
probably be most correct to assume the index to be -46 for the 
conditions of the present series of experiments. 
12. Relation between hydraulic radius and velocity.—As it was 
impossible to maintain the hydraulic radius absolutely constant 
throughout the series of experiments on the effect of slope, an 
auxiliary investigation was made to determine the method of 
variation of velocity and hydraulic radius. Owing to the acceler- 
ation of the rate of flow at the higher value of the hydraulic 
radius, as described in the preceding section, it was not feasible 
to make use of a wide range of values, and hence the expression 
arrived at from these experiments is to be considered, not in the 
light of a general expression showing the relationship between the 
hydraulic radius and velocity, but merely as a sufficiently good 
approximation for purposes of correction. As will be made evi- 
dent by the accompanying curves (A and B) the approximation 
obtained is a very close one. ‘Two series (A and B) of expert 
ments were made at, slopes of ‘0663 and ‘02213 respectively. 
The results are summarized in Table VII. 
Table VII. 
Series A._Slope = ‘0663. Temperature = 18°C. 
Number 
i Me: : 
in Series. | Velocity.) Log U | yyg tadins.| LoS R Sections. 
2 80°3 | 19047 | “464 | 16665 | D, EZ, F, G 
1 | 101°0 | 200482 639 =| 1/8055 
1182 | 20726 | ‘796 | 19009 | » » » » 
125°9 | 2:10009) = -884 19464 | Interpolated 
’ 
” ” ” ”? 
3 
TE. at 
Series B.—Slope = ‘02213. Temperature = 18° C. 
49-7 | 1°6963 “478 16794 | D, BE, F, G 
1°7931 "658 1°8182 ” oan ae 
i 
976 EME 9 
5 784 | 18943 "952 19786 | Interpolated 
e 86-4 | 19365 | 1040 0170 | D, E, F, G 
