Measurement and Division op Water. 27 
the depth of water flowing over the weir. It is difficult to measure 
directly. The tests to determine its amount were unsatisfactory and 
consequently weirs are sometimes made to eliminate lateral 
contraction entirely. On the assumption that the contraction 
is one-tenth of the depth the calculated discharge agreed so 
closely with the measurements as a whole that this convenient factor 
was adopted. If there are two contractions, one at each end, the 
reduction of length would correspond to one-fifth of the depth of 
water flowing over. With this assumption the flow may be found 
within one per cent, within the limitations given by Francis. 
Thus we may take an example from the abstract of Francis’ 
experiments on page 25. In the case of the serial numbers 1-4, the 
depth is 1.56 feet. There are two contractions, hence the effective 
length of the weir used in the calculation of the discharge, is not 10 
feet, but 10 feet shortened by .31 feet (2, the number of contrac¬ 
tions, x 1/10 of 1.56). The effective length to be used in the cal¬ 
culation is accordingly. 9.69 feet. With the same weir, in the series 
56-61, the effective length is 9.84, though the length of the weir is 
the same in both cases. 
It is because of the correction to the length in the rectangular 
weirs in the Francis formula that the weir method of measurement 
was slow in being adopted. It is evident that a weir twice as long 
as another will give more than twice as much water, with the same 
depth. This proved a stumbling block in the popular mind, and 
stood in the way of its use. 
The advantage of the Cippoletti form of trapezoidal weir is 
that the discharge varies directly as the length of the weir, so that 
if one weir is twice as long as another, the discharge will be twice 
as great. This is a great practical advantage in its use on canals, 
because it helps to lessen the suspicion frequently met with. 
This weir is one proposed by the Canale Villoresi, one of the 
great Italian canals in the valley of the Po. This canal was built 
about 25 years ago as a “high-line” canal to water land above 
existing ditches. It waters about 125,000 acres just north of Milan. 
In the permit to this canal, the company was required to propose 
a module based on the weir. The problem was put in the hands 
of Cesare Cippoletti, the engineer in charge of construction, who, 
from the experiments of Francis, attempted to determine a form 
of weir and conditions so that the results would be correct enough 
for ordinary purposes, and so that no single cause would produce 
an error of one-half of 1 per cent. This is often spoken of as a 
trapezoidal weir but because there are many forms of trape¬ 
zoids, I proposed that the name of the engineer should be con¬ 
nected with it, in the first edition of the Bulletin, and it is now 
