30 
The weir measurement is accurate, provided the proper con¬ 
ditions are observed , but the conditions for the construction of 
weirs are not generally known, and less generally observed. 
It should also be understood that it is safe to apply the for¬ 
mula only within the limits of the experiments on which it is 
based. I he results either by the weir or other orifices, are 
exact only so far as our experimental knowledge goes. The 
theory oi the flow of water under even the simplest con¬ 
ditions is still too incomplete, and the laws too imperfectly 
understood to allow of passing much beyond the data with 
which we are possessed. In order that a weir formula should 
apply beyond these limits, the value of the coefficient a , in 
the formula would be a varying one. In the Francis formula 
the coefficient is given a constant value, the disturbing effect 
of the side contraction being taken into account by varying 
the value of L. But if the weir be placed so as to meet the 
following conditions, the formula above given, and the tables 
attached to this bulletin, may be used with confidence that 
the result is correct within i per cent. 
CONDITIONS FOR THE WEIR, EITHER RECTANGULAR OR 
TRAPEZOIDAL. 
In nearly all cases, the weirs placed for measurement, 
are not placed with sufficient care to make the measure¬ 
ment one of great accuracy. The present demand for water, 
which is to increase, will gradually require more care in 
every detail. The weirs commonly used are of timber with 
board sills and sides, not usually made in a wide enough or 
deep enough channel. 
With the more pressing demand for exact measurement 
which is coming already in Northern Colorado, companies 
will soon be justified in constructing permanent weirs, with 
much care. Fnder the Canale Villoresi where the Cippoletti 
weir was first used, all the weirs examined by the writer were 
construced of cut stone, and the crests and sides were made 
of iron plates, the whole made with care so as to remain use¬ 
ful for generations to come. 
* If the following conditions are followed in constructing a 
weir, whether it be rectangular or trapezoidal, the weir for¬ 
mula may be used with confidence that no single cause will 
produce an error greater than one half of i per cent. The 
conditions are essentially the same as those either of Francis 
or of Cippoletti.* 
i. T hat the channel leading to the weir be of constant 
cross-sectio n, its axis passing through the middle of the weir, 
*Canale Villoresi, Modulo per la Dispensa delle Acqua, etc, Milan 1886, pub¬ 
lished by the Societa Italiana per Condotte d’Acqua. 
