MEASUREMENT AND DIVISION OF WATER, 
21 
formula indicated by his experiments lias since been 
standard within the limits indicated by him. If one ob¬ 
serves the flow of water through an orifice he will observe 
that the stream becomes narrower, or is subject to lateral 
contraction. If over a weir, the sheet of water becomes 
thinner immediately below the crest, as in fig. 6, or is sub¬ 
ject to a vertical contraction. By taking separate account of 
these two contractions Francis succeeded better than pre¬ 
vious experimenters in producing a formula which 
represented the discharge. The form of the equa¬ 
tion indicated by theory and agreeing closely with 
Francis’ experiments is of the form, 
3 
Q = a L H 2 
Where Q = the quantity of water flowing in cubic 
feet per second, L = the effective length of the weir in 
feet. This is not necessarily the same as the actual length 
of the weir. 
H — the depth of water flowing over the weir in feet. 
Because of the contraction shown in fig. 6, this must be 
measured far enoughjfrom the weir to be free from its in¬ 
fluence. If the water approaches with a current* this depth 
needs to be increased by a correctionfindicatediby^theory. 
This correction is troublesome to make.1! In|practice~ it is 
better to so reduce the velocity of the current that the cor¬ 
rection may be neglected. 
a is a numerical coefficient which is needed to multi¬ 
ply the result obtained by the indicated operations in the 
measured quantities, in order to give Q the discharge. 
