A NEW EVAPORATION FORMULA 107 
0.001 foot as in this evaporation investigation, A , 1 = (0.00G0)xf 1 ^-) = 0.. r )5. 
If it is now assumed that part of the evaporation in these two months is represented 
by the [«(t|t) 
i 
Ei — term, the value of E, may be arbitrarily reduced to 
0.50, as this value lends itself easily to calculation. The value of E 2 was arbitrarily 
assumed to be 4 as large as E t or +0.20 in the first solution. These values were 
revised many times from the actual observations in the many least-square solutions 
which preceded Solution V x before the values assumed in that solution were secured. 
The first estimate of values of R x , R 2 , R>, . . . Rt to use in the first least-square 
solution was nothing more than a guess. The internal evidence from the succeeding 
least-square solutions gave positive proof that this original estimate was too large. 
Accordingly the values were reduced in each succeeding solution so long as the 
evidence persisted in proving the assumed values still too large. Solution Fi 
represents the eighth least-square solution on Lake Michigan-Huron in which 
observation equations of the form of (28) was used. In these eight solutions, the 
original estimate of the R's was revised several times before the final values, (29), 
were secured. As will be shown later, these values are still probably much too 
large. 
The principal type of evidence from the least-square solutions which indicated 
an assumed set of R's to be too large was the fact that the estimated run-off as 
shown in column 12, Table 37, would sometimes come out negative. Theoretically, 
negative run-off would be an absurdity. It would correspond to a slope of the 
water "table," downward from the lake, instead of downward toward the lake. 
This condition might exist locally, but probably not generally for the whole lake 
region. Also a ground-water level sloping downward away from a lake or reservoir 
surface could exist in the case of a lake located on top of a hill or mountain — a lake 
whose content was maintained by precipitation directly upon its surface, and 
whose only outlets would be, say, seepage and evaporation. 
The observed rainfall on the land drainage area tributary to the lake, used in 
computing r 1} r 2 , r 3 , . . . r 6 was obtained from observations made at the 142 
stations shown in Table 5 and on Plate 1. The rainfall observed at each station 
in inches was multiplied by the station-factor shown in Table 5, and the sum of 
these products gave the rainfall on the land drainage area in units of 100 inch-miles. 
This was then converted to units of 0.001 foot of depth on the lake surface by 
multiplying it by the factor 0.184. Except for the conversion stated in the preced- 
ing sentence, the computation was exactly analogous to the illustration given of 
the computation of the rainfall on the lake, I 2 , shown on pages 32 to 38. 
The rainfall, computed as stated in the preceding paragraph, is shown in 
column 14, Table 37, preceded by a negative sign. 
To compute — r x for any day, one adds together algebraically the three quanti- 
ties — (observed rainfall), + (estimated evaporation from land), and + (estimated 
run-off) for that day. The method of computing the first two quantities has been 
explained. 
Estimated run-off for any day, shown in the twelfth column of Table 37, is 
the sum of the constant part of the run-off, / c = 6, shown in column 5, and the 
variable part of the run-off, Rir l +R 2 r 2 -\-R 3 r 3 + . . . -\-R 6 r e , shown in columns 6 to 
11 inclusive, computed by multiplying the assumed values of R x , R 2 , R 3 , . . . R 6 , 
(29), into the computed values of r,, r,, r 3 , . . . r„ respectively. To be specific, the 
