Measurement and Division of Water. 29 
The weir measurement is accurate provided the proper 
conditions are observed , hence the importance of an understanding 
of the conditions and their careful observance, both in construc¬ 
tion and in operation. The formulae are most reliable only within 
the limits set by Francis, that is, within depths ranging from 3 
to 24 inches for complete contractions, and for weirs not much 
exceeding 10 feet in length, but subsequent tests show that they 
may be used for greater depths and lengths without material error. 
The theory of the flow of water under even more simple conditions 
is still too incomplete to make it safe to extend the formula much 
beyond experimental lines. Within these limits the coefficient may 
be taken as constant. Outside of these limits, the coefficients would 
probably require a different value. In the Francis formula, the 
coefficient is taken as constant. 
In most cases weirs are not placed with sufficient care. On 
the Canale Villoresi, the weirs I examined were made of cut stone 
with cast iron plates used for the sides and sill. The value of water 
justifies the construction of permanent and substantial weirs in 
this State and much more pains than is generally taken. 
Conditions. —The following conditions relate to both types of 
weir. When these conditions are followed, the formula above given 
and the tables attached to this Bulletin may be used with confidence 
that the result is correct within 1 per cent. 
1. The channel leading to the weir should be regular, of constant 
cross-section, its axis passing through the middle of the weir, and per¬ 
pendicular to it; this straight reach to be of such length that the water 
flows with uniform velocity, without internal agitation or eddies. This 
should be not less than fifty or sixty feet in length, more if possible. 
2. The contraction should be complete on both sides and bottom. 
This is necessary that the coefficient “a” in the formula may be free 
from uncertainty. To secure complete contraction it is necessary: 
(a) . That the opening of the weir be made in a plane surface, 
perpendicular to the course of the water; 
(b) . That the opening itself have a sharp edge on the upstream 
face. For this purpose, if the thickness at the point of discharge is not 
more than one-tenth the depth for depths from 5 to 24 inches, it may 
be considered as sharp; 
(c) . That the height of the sill of the weir of the canal be at least 
three times the depth of water on the weir; 
(d) . That the length of the weir should be three, or still better, 
four, times the depth of the water flowing over; 
(e) . That the depth of water flowing over the weir be not less 
than 3 inches; 
(f) . That distances from the sides of the flume shall be not less 
than 2 times the depth. 
3. The velocity of approach must be small. For weirs three feet 
long and depth of 12 inches, it ought not to be more than one-half foot 
per second; for weirs of six feet long and depth of 24 inches it ought 
not to be above 8 inches per second. In all these cases the cross-section 
of the canal of approach ought to be at least seven times that or the weir. 
Other conidtions affecting the velocity of approach are included in c, d 
and e in condition 2 above. 
4 The layer of falling water should be perfectly free from the 
