STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 353 
23. The index of roughness (n) probably a function of the slope 
(Z) in open channels.—We may test this as above indicated. From 
an extensive series of interpolations from series 6, 7, 8, 9, 10, 11, 
18, 19 and 20, of Bazin’s experiments with channels formed of 
ordinary boards, after very small corrections for hydraulic radius 
and temperature, I have taken the following results :— 
Form of channel = depth/breadth =A; log R 2°867. water 11°C. 
log J 3176 3-318 3-690 3-771 3-916 3-924 
log OU 1°757 1-862 2-081 2-183 2-213 2-219 
This gives as a mean result n= 1-643, but there is some indication 
of ” increasing with J. 
Again, Series 6, 7, and 8 were made at the temperatures 7, 83, 
and 82° ©, respectively, the breadth of the channel—199 cm.— 
and materials—boards—being the same in each case. Forming 
by logarithmic interpolations, the values of log U for the three 
slopes, for the hydraulic radii whose logarithms were 1-00, 1:14, 
108, 1-21, 1-26, 1:28 and 1-29, we find no indication of variation 
with the hydraulic radius. It is therefore legitimate to take the 
mean of the differences of the logarithms, which gives the follow- 
ing results:— 
(a) log J, — log J, = -327 log I, - IZ, = ‘226 
(5) mean diff. log U = 222 120 
nm = say a/b = 1-47 1:88 
The slopes are -00208, -00490 and -00824 so that apparently 
increases with J. A similar indication is also given by series 9, 
10 and 11, in which the breadth of the channels and material are 
the same. 
The very small range of slope in Bazin’s experiments, and the 
want of a sufficient number of experiments throughout that range, 
points out the desirability of hesitating as to the assumption ee 
® varies with the slope in channels though not in pipes. Experi- 
ments in order to determine this point are necessary. They 
should of course be made, as pointed out, preferably with triangular 
channels of constant inclination of sides, and necessarily of constant : 
W—Deec. 1, 1897, 
