io8o 
Journal of Agricultural Research 
Vol. V, No. 23 
The curves and the table show that with heads less than one-third 
the length of the crest the Cipolletti formula gives discharge values within 
1.5 per cent of the actual discharges, therefore being somewhat more 
accurate than the Francis formula. The new formula, like the new 
formula for the rectangular weir, is not only more nearly accurate than 
the old formula, but also permits the use of heads greater than one-third 
the crest length. The maximum limit of the ratio of the head to the crest 
length was not ascertained, but the parts of the curves for the higher heads 
are consistent, there being no sudden breaks or changes of direction. 
The new formula is more complicated than the Cipolletti formula, but 
because of its greater degree of accuracy it should be used in computing 
tables. The Cipolletti formula, however, is sufficiently accurate for field 
computations where only approximate discharge values are required. 
Cipolletti notches do not give discharges proportional to the lengths 
of the crest, as has been commonly claimed, and consequently notches 
of this type have no advantages over rectangular notches (seep. 1098). 
Formula Based on the Straight-Line Formula for Rectangular Notches 
The difference between the discharges computed by the new rectangular- 
notch formula and the discharges taken from the curves plotted from the 
experimental data for the Cipolletti notches were determined for each 
0.1 foot of head for the several lengths of notches. These values were 
then plotted logarithmically against the heads, and the equation of the 
average straight line representing the difference in discharge was found 
to be D=.6if 2 * 6 . By adding the term 0.6/P 6 to the general formula 
for discharges through rectangular notches (p. 1071), the general formula 
for discharges through Cipolletti notches was found to be 
0 = 3.o8L 1 - 022 H< 1 - 46+0 * 003L ) + 0.6H 2 * 
This formula gives discharge values that agree within a maximum of 
1 per cent of the values indicated on the curves plotted from the experi¬ 
mental data, but the agreement is within 0.5 per cent for all but a very 
few points. 
Table VIII gives the discharges through the notches used, computed 
by the two formulas deduced for the Cipolletti notches, and the dis¬ 
charge values indicated on the curves plotted from the experimental 
data. 
