INVESTIGATION OF FLOW OF WATER IN UNIFORM CHANNELS. 367 
to the water surface, for determining the area, were obtained 
probably to ‘01 cm. (as explained in § 6) so that, on the extreme 
assumption that the errors were made on the same side all along 
the surface, the resulting error would be about 8-0 x ‘01 = 08 sq.cm. 
in the case of Series I., and about 6-0 x ‘01 = 06 sq. em. for Series 
II. The average areas for these two cases are approximately 
20 sq. cm. and 7 sq. cm.; hence the degree of error involved 
on the above assumption, in determining the area would be about 
1 in 250 and 1 in 120 respectively. The actual errror is probably 
less than this. The quantity subject to the most uncertainty in 
the investigation is the wetted perimeter, owing to the difficulty 
experienced in deciding exactly where the mean edge of the stream 
occurred. This difficulty of course decreased as the slope was 
diminished and the corrugation of the surface consequently was 
less marked. The average error in the side reading would not be 
greater than -3 mm. corresponding to an error in the wetted 
perimeter of about one per cent. The wetted perimeter itself 
was determined by scaling from the plots of the channel sections 
previously referred to. The hydraulic radii were then determined 
for each section, and the velocities were reduced to a common 
radius of 1-5 cm. in Series I., and 1-0 cm. in Series II., by means 
of the law obtained from Series A and B. 
The slope, J, was assumed to be that of the water surface, the 
levels to which were obtained as described in § 8 to “01 cm. In 
nearly every case the slope was taken over a distance of 300 cm., 
8o that the error of slope involved is about -000033. The lowest 
slope used in determining the law of variation of slope with velocity 
was about ‘007 the degree of uncertainty in which is therefore 
33 in 7000, or a little less than 1 in 200. As the slope increases 
the degree of error diminishes, it being reduced to 1 in 2000 at a 
slope of -066, which was the greatest slope used. The temperatures 
were obtained by means of two mercurial thermometers graduated 
in degrees Fahrenheit and provided with Kew certificates of date 
June, 1893. The readings were then reduced to degrees centigrade. 
€ maximum correction to be applied to the thermometers was 
