22 
MEASUREMENT AND DIVISION OF WATER. 
From his experiments Francis adopted for this co¬ 
efficient the value, a = 3.33; though 10-3 would agree 
more closely with his results, and it seems to the writer 
to be more convenient for calculation. 
The formula of Francis then becomes 
3 
Q = 3.33 LH 1 
where the letters mean the same as in the formula on the 
previous page, and with the same restrictions. 
END CONTRACTION. 
An additional word needs to be said regarding L, the 
effective length of the weir. The contraction of the 
stream passing over the weir has already been mentioned. 
The contraction is said to be complete when the sides and 
walls are so far away as not to affect it; incomplete when 
so affected, or no contraction, as when the weir is in the 
lower end of the flume and extends the whole width. 
The contraction should be complete or none at all. 
If no contraction the full measured length of the weir 
is used. 
If complete, the length of the weir is diminished by 
one-tenth of the depth for each contraction. The con¬ 
tractions usually occur in pairs, one on each side of the 
opening. If the opening he broken into two parts or 
hays there may be four contractions. Thus, in Series A 
of Francis’ experiments, given on page 24, the length of 
the weir being 10 feet and the depth 1.56 feet, the two 
contractions reduce the length by 2-10 of 1.56 feet, the 
depth, or 0.31 feet. L, the effective length to be used in 
the calculation, is then 9.69 instead of 10 feet. 
It is best to have complete contraction, the conditions 
of securing which are given in Nos. 4 and 5 of the fol¬ 
lowing conditions. While it is generally believed that 
this formula is accurate, it is not so generally understood 
