25 
these two contractions, Francis succeeded better than previ¬ 
ous experimenters in producing a formula which represented 
the discharge. The form of the equation indicated by theory 
and agreeing closely with Francis’ experiments, is of the form. 
O^aLui 
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. It 
is mentioned more fully on the next page. 
H=the depth of water flowing over the weir, in feet. Be¬ 
cause of the contraction shown in Figure 6, this must be 
measured far enough from the weir to be free from its influ¬ 
ence. If the water approaches with a current, this depth 
needs to be increased by a correction indicated by theory. 
This correction is troublesome to make. In practice it is bet¬ 
ter to so reduce the velocity of the current that the correction 
will be so small that it may be neglected. Table II. in the 
appendix gives the amount of this correction in different cases. 
^ is a numerical coefficient which is needed to multiply 
the result obtained by the indicated operations in the meas¬ 
ured quantities, in order to give O the discharge. 
From his experiments, an abstract which cannot convey 
an idea of the care and skill used in the experimentation, 
Francis adopted the value of 3.33 for a\ would agree a 
little more closely, and is slightly more convenient for inde¬ 
pendent calculation. The value of 3.33 is almost universally 
adopted. 
The formula of Francis then becomes 
where the letters mean the same as above and with the same 
restrictions. 
O represents the discharge in cubic feet per second. 
L and H are both measured in feet and decimals. 
Sometimes it is convenient to make measurement of the depth in inches. 
Scales giving decimal parts of feet are not common. In such case the following 
formula may be used. Q is the discharge in cubic feet per seeond in both cases. 
Where chvtli is measured in inches, and length of the weir is given in inches, then 
3 
Q (sec. ft.)=-.0798 L (in inches) H ^ (in inches.) 
Where depth is measured in inches, but the length is given in feet. 
3 
Q (sec. ft.) .006675 L (in feet) H ^ (in inches.) 
An additional word needs to be said regarding L. 
L is the effective length of the weir, which in case of the 
rectangular weirs, is not necessarily the same as the actual 
length. 
