SPILLWAYS FOE RESERVOIRS AND CANALS. 7 
This is not surprising when it is seen that only one of the factors 
entering into the formulas cited is fixed by the form of the structure. 
It has been stated that in the process of gaging streams at dams the 
head is usually measured in comparatively still water in an open pond, 
but this is an assumption at best and must be corrected to conform to 
an assumed velocity of approach. In this connection it may be well 
to mention that the more complicated Bazin formula quoted in an- 
other part of this paper includes the correction for velocity of ap- 
proach in the weir coefficient, and therefore the coefficient for a given 
weir is comparable only with the coefficient of another weir under the 
same head when the velocity of approach is the same in both cases. 
The Bazin formula also expresses the velocity of approach by means 
of the depth and breadth of the leading channel, which is rarely if 
ever of regular form so that the use of such an unreliable base is 
questionable. It is not the intention to discuss in this paper the 
relative values of the different formulas with their corresponding 
exponents and coefficients to apply in the various cases, but it is at- 
tempted to point out the great number of factors to be considered in 
the design of a spillway to keep the pond level within limiting bounds 
and at the same time perform its fluty as a safety valve in times of 
excessive stream discharge. The uncertainty arising from the use of 
these formulas and the assumption of the maximum quantity of 
water to be discharged emphasize the need of using a liberal factor of 
safety in the protection of that part of the structure to be guarded. 
At best the result is merely an approximation. 
Overflow spillways seldom are fully satisfactory on a canal system, 
since their crests are ordinarily built parallel to the center line of the 
canal, and to produce the effect of a normal canal supply the depth 
of water in the spillway over the lip would have to range from the 
maximum depth above normal surface in the canal at the upper end 
of the spillway to no depth at all at the lower end. Otherwise the 
canal would still be above normal supply beyond and below the 
spillway, and to produce full efficiency the crest of the spillway 
would have to be abnormally long. The writer has observed that 
the depth on the crest of most canal spillways is practically the 
same at both ends unless a long crest is built, which adds greatly to 
the cost. The use of an abnormally long spillway on a canal to dis- 
charge the water in excess of the normal supply, or above important 
structures where overflow would be particularly serious, requires the 
addition of costly and extensive training works and channels to di- 
vert and convey the wasted water to some natural drainage channel. 
Economy has been approached in some cases by the construction of 
the upper portion of these conveying channels parallel to the center 
line of the canal or spillway, or by building the spillways in a den- 
tated form to gain crest length and at the same time reduce the area 
