Mar. 6,1916 
Flow through Weir Notches 
1059 
repeated until such agreement was obtained. It is not claimed that 
this arbitrary rule insures the accuracy of results of the individual tests, 
but it did lead to the detection of irregularities in the working conditions 
and increased the probability of accuracy. Comparatively few tests 
had to be rerun, which indicates the stability of the experimental tests 
and the nice control of the heads made possible by the head gates, 
wasteways, and baffles. 
The heads and the corresponding discharges obtained were plotted 
for the various notches. The curves were then drawn which best rep¬ 
resented the discharges through the different notches, the plottings 
being made upon such a scale that discharge values could be read from 
the curves to three decimal places. 
The following method was used in smoothing the curves and obtain¬ 
ing the values for C in the general formula Q=CLH n : 
Discharge values were taken from the curves for each 0.05 foot head, 
and the slope was determined for each straight line connecting pairs of 
points. The slope for each point was first taken as the average between 
the slopes of the two straight lines to which it was common; then, calling 
the point in question b , the point for the next 0.05 foot head above, a, 
and that below, c , the slopes were given a second smoothing by the 
equation a ^~ 2 ^~^ c =b; and a third smoothing was obtained by substi¬ 
tuting the values obtained by the second smoothing in the equa¬ 
tion a ~^ 2 ^ c These values were plotted, and the equation 
of the resulting curve was used to compute the last smoothing of the 
slopes. Substituting these computed values for n in the general formula 
Q = CLH n y the corresponding value of C was obtained for each head. 
EXPERIMENTS WITH NOTCHES HAVING FREE FLOW 
DEDUCTIONS OF FORMULAS FOR RECTANGULAR AND TRAPEZOIDAL 
NOTCHES 
The general type of formula heretofore used for discharges through 
rectangular and trapezoidal notches is Q = CLH n , in which L is length of 
crest, H the head of water over the crest, and C and n are constant for 
each type of weir. Expressed logarithmically, the general formula be¬ 
comes log Q = log C + log L + n log H, which equation, when plotted, 
gives a straight line whose slope is n and whose intercept is log C+log L. 
The data obtained for the rectangular and Cipolletti notches, when 
plotted logarithmically, gave curves instead of straight lines. It was 
found, however, that a general straight-line equation could be deduced 
for the discharges through the rectangular notches, which, within the 
range of the experiments, would give discharges as close to the experi- 
