27 
is two or three times the depth on the weir, there seems to be 
no further change in the contraction with the increased dis¬ 
tance. In such case, the contraction is said to be complete. 
Prom the case of complete contraction theie may be all de 
grees of contraction down to no contraction. 
The amount of this contraction, when complete, inci eases 
with the depth of water flowing over the weir. It is diflicult 
and unreliable to measure the amount directly. But we again 
have recourse to the experiments of Francis, from which it is 
determined that with complete contraction, and the same lor- 
mula, that if an allowance be made, equivalent to a shorten¬ 
ing of the weir equal to one-tenth of the depth of the water 
flowing over it, for each complete contraction, the discharge 
Figukk 7. 
will be given, other conditions being correct, within i percent. 
Thus, we may take an example from the abstract of 
Francis experiments, given on page 26. 
In the case where the depth is 1.56 feet, there are two 
contractions, hence the effective length of the weir, or the 
length to be taken in the calculation of the discharge, is not 
ten feet, but ten feet shortened by two (the number of con¬ 
tractions) times one-tenth of 1.56 feet; or .31 feet less than iq 
feet. The effective length is accordingly 9.69 feet. With the 
same weir, but a depth of .80 feet, the effective length, or the 
