Measurement and Division or Water. 41 
APPENDIX. 
EXPLANATION OF TABLES. 
Tables I. and II. are to give means of correcting the errors to the 
velocity of approach without the troublesome calculations indicated in the 
text. 
Table I. gives the average velocity through the opening of a weir for 
different depths. It may be used to determine the velocity of the water as 
it approaches the weir. This may be found by comparing the cross-section 
of the channel of approach with the cross-section of the weir. If this is 
the same then the velocity given in the table would also be the velocity of 
approach. If the cross-section is, say, three times the area of the weir, 
then the velocity would be one-third of that given in the table. If the 
eross-section is seven times as great as the weir, as recommended in the 
text, then the velocity of approach would be one-seventh of the average 
velocity in the section of the weir, and thus for depths of two feet, the 
velocity of approach would be less than three-fourths of a foot, in which 
case the correction would be small. 
Table II. is computed from the Fteley formula and expresses the cor¬ 
rection to be given to the results of Tables III. to VI., due to the velocity of 
approach. This correction is expressed in per cent. The formula is based 
on experiments limited to 2.5 feet per second. 
Tables III. and IV. give the discharges over weirs of unit length. The 
discharge of weirs of any length may be obtained by multiplying the quan¬ 
tity given for the proper depth in these tables by the length of the weir. 
This would apply more especially to the Cippoletti weir. If correction for 
contraction is made, then the length should be decreased by one-fifth of 
the depth of the water. In both these cases, depths are measured in 
inches, the formulae being given on page 2 3. 
Table V. gives the discharge over rectangular weirs, from 1 to 10 feet 
long. In this case the discharge with two complete contractions is given 
and thus, in order to obtain the same result as in Tables III. or IV., the 
correction in the last column would be added to the results in the previous 
columns, or it could be subtracted from the result as obtained by the use of 
Tables III. and IV. 
In both Tables III. and IV. the discharge is computed for every one- 
sixteenth of an inch. In this case the whole inch is given at the left and 
the sixteenths are given at the head of the page. 
Example: What is the discharge over a weir 45 inches long and with 
a depth of 11 44 inches with tw r o complete contractions? 
Find 11 inches at the left of the page, and the column headed one- 
fourth inch at the head of the page. Follow this column down until it in¬ 
tersects the line of the 11. At the intersection is the discharge, for a por¬ 
tion of the weir one inch long, which is .2 519 cubic feet per second. Then 
for a weir 45 inches long it is 45 times as much, or 11.3345 second feet, 
if without contraction. The second column gives the allowance for con¬ 
traction for 11 inches depth; the eleventh column for a depth of 11% 
inches. For 11% inches we then take a value intermediate between those 
for 11 inches and 11% inches, obtaining the correction .567, the amount 
by which the discharge is reduced. This, then, leaves the total discharge 
as 11.335—.567 or 10.77 second feet. 
Table VI. is for Cippoletti’s trapezoidal weir and thus differs from 
Table V. in not allowing for contraction, as given in the last column of 
that table. It is also one per cent, greater. 
It will be noticed that the discharges in Table VI. are directly pro¬ 
portional to the length of the weir, while in Table V. they are not. The 
quantities in Table V. were computed with the coefficient 3% instead of 
3.33 of the Francis formula. 
Table VII. gives the discharge through right angled notches. 
Table VIII. is to enable measurements made in inches to be expressed 
in decimals of feet. 
