1052 
Journal of Agricultural Research 
Vol. V, No. 23 
or Francis type, and the Cipolletti type. Most of the weirs in use have 
notches with crest lengths of 4 feet or less, being such as are adapted to 
the delivery of water for farm units. Unfortunately, owing chiefly to 
the confusion of the statements contained in the literature on weirs, 
various standards of dimensions have been used in the construction of 
the weirs now in use. This lack of uniformity results in many erroneous 
measurements. 
The basic experiments with notches having thin edges and full con¬ 
tractions were made by James B. Francis (5) 1 from 1848 to 1852. These 
have subsequently been enlarged upon by several experimenters and 
mathematicians. Francis made three series of experiments with rec¬ 
tangular-notch weirs, but the discharges were measured directly in only 
one series (5, p. 75-76). In each of the two other series an equal flow 
of water was made to pass through notches of different lengths, the crest 
lengths and the heads being noted. In the experiments, where the dis¬ 
charges were measured volumetrically, only notches of approximately 8- 
and io-foot lengths were used, and the heads ranged from only 7 to 19 
inches (5, p. 122-125). Most of the experiments were made with the 
io-foot notch, as they were to be applied directly to the measurement 
of water for power purposes. Francis stated (5, p. 133) that the formula 
which he derived would apply to heads ranging from 6 to 24 inches, but 
in no case was it to be used either for heads exceeding one-third the 
length of the crest or for very small heads. With these limitations the 
formula can not be used for weirs having crest lengths of less than 1.5 
feet nor for heads exceeding 2 feet. For a 1.5-foot crest the formula can 
be used only for a 0.5-foot head. Horton states (7) that the Francis 
data and formula will hold for heads from 0.5 foot to 4 feet. Francis’s 
experiments were very carefully and conscientiously made, but were 
with longer notches and greater volumes of water than are usually 
needed in delivering water to irrigators. The Francis formula is fre¬ 
quently used, however, without regard to the limits which he imposed 
upon it, and it is not uncommon to see tables computed from it that give 
discharges for heads as low as 0.01 foot, with heads as high as 1 foot for 
a crest length of 1 foot, and for crest lengths varying from 0.5 foot to 
20 feet. 
The most popular weir notch has been the trapezoidal type with side 
slopes of one horizontal to four vertical. This type was designed and 
the formula deduced by the Italian engineer Cesare Cipolletti (3), with 
the idea of automatically eliminating the correction for end contractions 
necessary with the rectangular notches and thus obtaining a type of 
notch the discharge through which would be proportional to the length 
of the crest and free from error in excess of one-half of 1 per cent from 
any single cause. Cipolletti derived the shape of the notch by a mathe¬ 
matical modification of the Francis formula for the rectangular notch. 
1 Reference is made by number to “Literature cited," p. 1112-1113. 
