366 S. H. BARRACLOUGH AND T. P, STRICKLAND. 
were then read at each centimetre graduation of each section, 
and the side readings to the edge of the stream were also taken. 
At the conclusion of a set of readings at any cross section, the 
time and head on the orifice were observed. A second set of levels 
was then taken, the temperature of the water was observed, and 
supposing the gauging tank to be nearly full, the stream was 
diverted to the drain, the time being again accurately noted. A 
final reading of the scale on the gauging tank completed the 
experiment, 
10. Reduction of observations, and degree of precision attained. 
—The quantities to be determined from the observations are (1) 
the mean velocity =U, (2) the mean hydraulic radius= 2, (3) the 
average slope = J, and (4) the temperature= 7’. Of these quantities 
if A be the mean area, P be the wetted perimeter, and Q/t the rate of 
discharge, the velocity and hydraulic radius will be respectively 
as -, and & — 
To determine the velocity therefore Q, ¢ and A have to be measured. 
The method of measuring Q has been detailed in § 7. Assuming 
that an error corresponding to ‘01 of a cubic foot is made in read- 
ing the scale on the gauging tank, and remembering that on an 
average 30 cubic feet of water were run into the tank for each 
experiment, the error involved is about 1 in 1500. The time, 4 
during which the water was running into the gauging tank varied 
from ten minutes at the greatest slopes to one and a-half hours at 
the smallest. If it is assumed that an error of one second was 
made in the measurement of the time interval—an assumption 
probably erring considerably on the right side—the degree of 
uncertainty involved varies from about 1 in 600 to about 1 in 5000. 
U 
In calculating the area, A, at each section, it was considered a8 
consisting of a series of trapezoids (one centimetre wide) together 
with three small triangles, viz., one at each side of the stream, 
and one at the bottom which was constant for any section. This 
latter area was obtained from an accurate plot of the cross section 
of the channel at the stations B,C, D, Z, Fand G. The ordinates 
