FOKEST COVEE IN PROTECTING RESERVOIRS 
11 
turbidity of the impounded stream and the rate of deposit of silt in 
the reservoir are such that three-fourths of the storage capacity, or 
24,000,000 kilowatt hours of potential power a year, will be lost 
within 40 years. To what expense, if any, would the owner of the 
water rights be justified in going so that at the end of 40 years 
the reservoir would have three-fourths of the storage capacity or 
24,000,000 kilowatt hours of power a year? (Fig. 1.) 
In case erosion should continue unchecked, at the end of 40 years 
there would remain only 25 per cent of the initial utility value or 
8,000,000 kilowatt hours a year. The utility value is irrespective of 
whether amortization of the investment has been effected in whole or 
in part. The question then is : What sum could be expended by the 
owners of the reservoir, assuming that the purchasing power of the 
dollar remains unchanged, to give assurance of a utility value of 
$1,500,000 at the end of 40 years? This would be three-fourths of 
the original utility value, whereas, if erosion continued unchecked, 
there would remain a utility value of only $500,000. (Fig. 2.) 
For the sake of greater simplicity and clarity it is assumed : That 
it would be possible to plant in one year all denuded lands the erosion 
WATER LEVEL 
DAM 
Fig. 1. — Decrease in storage capacity of a reservoir by decades, due to silting, 
schem'atic 
from which is most serious, such planting taking place possibly 
during the construction of the reservoir so as to obtain immediately 
the continued full benefits of its lengthened utility; (2) that the 
rate of sedimentation in the reservoir proceeds at a constant rate 
until, except for the channel of the stream, it is completely silted 
up; and (3) that the utility value is abruptly decreased by one- 
fortieth at the end of each year. Actually, however, such a rate of 
silting is not constant. Sedimentation takes place at a diminishing 
rate as the reservoir fills in, as the area of slack water diminishes, 
and as the general current of the water through the reservoir in- 
creases; and the rate of sedimentation is also subject to great varia- 
tion due to the occurrence of high floods or to long periods of even 
flow, and on account of eddies and convective currents the deposit 
as a rule is irregularly distributed. 
As a result of planting, there is assurance of a utility value of 
$1,000,000 at the end of 40 years which otherwise would have been 
lost. Without planting, this value would have been gradually 
reduced year by year through the period of 40 years so that at the 
end of that time none of it would have remained. Consequently 
there would be a consecutive loss of storage capacity at the end of 
