104 A NEW METHOD OF ESTIMATING STREAM-FLOW 
the run-off, have been introduced, and (b) that the wind travel, w, applies to all 
wind velocities instead of being limited to wind velocities above x. In equation 
(28), 
?\ = (Observed rainfall on land drainage area tributary to lake) — (estimated evaporation 
from land) — (estimated run-off) on the current day, expressed in units of 0.001 foot 
of depth on the lake area. 
?- 2 = (Observed rainfall on land drainage area tributary to lake) — (estimated evaporation 
from land) — (estimated run-off) on the preceding day, expressed in units of 0.001 
foot of depth on the lake area. 
r» = (Observed rainfall on land drainage area tributary to lake) — (estimated evaporation 
from land) — (estimated run-off) on the day before the preceding day, expressed in 
units of 0.001 foot of depth on the lake area. 
r< = (Observed rainfall on land drainage area tributary to lake) — (estimated evaporation 
from land) — (estimated run-off) on the two days preceding the day named in defining 
r 3 , expressed in units of 0.01 foot of depth on the lake area. 
r s = (Observed rainfall on land drainage area tributary to lake) — (estimated evaporation 
from land) — (estimated run-off) on the four days preceding the two days named in 
defining r 4 , expressed in units of 0.01 foot of depth on the lake area. 
r 6 = (Observed rainfall on land drainage area tributary to the lake) — (estimated evapora- 
tion from land) — (estimated run-off) on the eight days preceding the four days named 
in defining r 6 , expressed in units of 0.01 foot of depth on the lake area. 
Ri is a physical constant which expresses the effect of the change in storage in the land part 
of the drainage area on the current day, r h on the rise of the lake surface that current 
day. 
Similarly, R 2 , R}, . . . R 6 , are physical constants which express the effects of the change 
in storage in the ground on the preceding day, day before the preceding day, . . . next 
preceding eight days, respectively, upon the rise of the lake surface the current day. 
The similarity between the run-off part of equation (28) and the stream-flow 
equations in Part II of this publication should be evident. 
It was proposed to determine the unknowns, R h Ri, . . . R t indirectly from 
the least-square solutions by successive trials. The unknowns Ei and E 2 were to be 
derived directly. The mean value of the wind travel determined statistically to be 
240 miles per day was to be adjusted by the least-square computations to that value 
which, in combination with the best values of the various unknowns, was to reduce 
2(« 2 ) to a minimum. 
The evaporation terms have previously been defined, and +7 is the same as 
defined on page 9, and shown in column 10 of Table 23. 
Equation (28) expresses the fact that the lake surface is caused to fall by the 
natural evaporation from it, which is assumed at first to follow the straight-line law 
expressed in the first two terms. It further expresses the fact that the lake surface 
is caused to fall by the negative of the run-off into it, as expressed by the 72-terms. 
If the total fall, on any day, as computed from all terms to the left of +7 is just 
equal to +7, that is to the observed rise of the lake surface corrected for wind and 
barometric effects, inflow, outflow, rainfall on the lake, and constant part of run-off 
into the lake, then the residual, v, on that day will be zero. 
EXAMPLE OF COMPUTATION OF r,, r 2f r 3 , . . . r 6 
From previous examples the method of computing all of the quantities in the 
observation equation, (28), except the run-off terms, r,, r 2 , r,, . . . r 6 , should be 
