26 The Colorado Experiment Station. 
These experiments have been made with such care that they 
are standard and are uniformly recognized as being results which 
can be used with confidence in discussions of the accuracy of the 
weir. 
The greatest depth tested was about 18 inches, and the least 
7 inches. Series A and B correspond to the ordinary cases. From 
these, Francis concluded that the coefficient to be used in the for¬ 
mula might be taken as 3.33 while the length L is not the length 
of the crest, but is less by an amount which increases with the 
depth of water over the weir. It is noticed in his trials that the 
length of the weir is less than the width of the canal, thus giving 
the conditions for what is termed a complete end contraction. 
Francis presented his formula (i. e., with the constant 
coefficient) as being applicable to cases where the depths do not 
exceed two feet nor fall short of three inches, and where the depth 
over the weir is small as compared with the length. 
Experiments have since been made at the Cornell Hydraulic 
Laboratory which show that this formula may be used without 
material error up to depths of four and even five feet on the 
weir, provided the other conditions are observed. In these cases 
the flow over these weirs has been measured by the discharge over 
rectangular weirs agreeing with the conditions fixed by Francis. 
Some explanation needs to be made concerning the contrac¬ 
tion of the stream and its effects on the flow. If water passes 
through an orifice it will be noticed that it becomes narrower at 
the opening and then expands. If it passes over a weir with 
a sharp edge, the sheet of water immediately below the crest 
becomes thinner. This is termed the vertical contraction. At 
the sides, it also narrows and then expands. This is spoken of 
as the lateral contraction. The amount of the lateral contraction 
becomes greater as the depth of water is greater. Francis attempted 
to take several disturbing effects into account in the correction to L. 
While the correction is not entirely satisfactory, it is close 
enough for practical purposes so that the formula may be used 
with confidence, provided the weir is placed according to proper 
conditions. The amount of the contraction is also affected by the 
distance that the sides of the box are from the end of the weir. 
In Francis’ experiment, the weir 10 feet long was in a box 14 
feet wide. If the box were narrower and the weir the same, the side 
contractions would be less and the effect is to increase the flow some¬ 
what. When the distance to the sides of the box is two or three 
times the depth of water on the weir, the contraction remains practi¬ 
cally constant and is said to be complete. If the box becomes nar¬ 
rower, the contraction is incomplete. 
The amount of this contraction when complete increases with 
