96 A NEW METHOD OF ESTIMATING STREAM-FLOW 
seventh column, but were computed from the original tabulation of e's and v's for 
the wind velocities concerned. This extensive tabulation is not shown for want 
of space. The mean value for each group shown in the second to last column was 
placed approximately opposite the center of gravity of the observations in that 
group, and the corrected E v shown in the last column was taken as the sum of the 
correction in the second to last column and that value of the computed E w in the 
sixth column which happened to be opposite it. The values in the last column are 
plotted in the upper part of Plate 6, and are represented by thecurve marked "Lake 
Superior" in the legend. This curve starts at the left with an evaporation of 
— 0.40 in terms of e for a 5-mile wind, rises to an evaporation of +0.02e at a 6.2- 
mile wind, falls to a minimum evaporation of — 0.59e for a 7.9 m.p.h. wind, and 
rises thereafter for increasing winds. 
The computation of the evaporation curve for Lake Michigan-Huron, com- 
puted from the results of Solution V t in the same manner as that just described for 
Lake Superior, is shown in Table 33 in the first to seventh columns, inclusive. The 
corrected total evaporation by large groups, shown in the seventh column, is 
plotted in the upper part of Plate 6 in the curve marked "Lake M-H" in the legend. 
It will be observed that this curve has the same general shape as the Superior curve. 
It has a peak between a 6 m.p.h. and a 7 m.p.h. wind, falls on either side, then rises 
continuously for winds above about 9 m.p.h. It differs from the Lake Superior 
curve, however, in that it shows an evaporation greater than zero throughout its 
extent. The two curves were combined into a weighted mean curve shown on 
Plate 6 by the curve marked "Weighted Mean" in the legend. The computation 
of this curve is shown in the last two columns of Table 33. The Lake M-H curve 
was given twice the weight of the Lake Superior curve, which is approximately the 
relative weights indicated by the reciprocal of the squares of the probable errors as 
shown in Table 31, 1-i-l ' J =1.7 - 
It is this weighted mean curve which is of prime significance in fixing upon the 
final form of the evaporation equation as used in all solutions subsequent to V 2 and 
BB 2 (Table 30, page 91). The peak in the curve at a 6.7 m.p.h. wind probably has 
no real significance. Nor has the depression at a 7.9 m.p.h. wind. These irregu- 
larities are probably due to accidental influences. If one consider the peak thrown 
into the depression, the curve may be considered as being roughly horizontal up to 
a wind velocity of about 9 miles per hour, after which it rises rather steeply. It 
could not reasonably be considered horizontal beyond a wind of about 1 1 miles per 
hour. These studies served to fix upon the range of wind velocities of from 210 
miles per day to 260 miles per day tested out in Solutions F, to V 6 and BB 3 and 
BBt. They not only indicated that the lower limit of wind velocity to use was less 
than 10 miles per hour, as did the direct evidence from Solution V 2 and other 
solutions with straight-line formulas, but they indicated the probable upper limit 
also, and besides showed the curve to be essentially horizontal at low wind velocities. 
From a consideration of the economics of the problem, the testing out of other 
wind velocities between 210 and 260 miles per day did not seem justifiable. Prob- 
ably very little gain in accuracy, if any, would result from the use of some other 
value than 2.6 for x. The true value may be 2.5. It is probably not greater than 
2.6. The value 2.6 was adopted at the culmination of Solutions V b and BB t as 
probably representing the best compromise between extreme accuracy, on the one 
hand, and large expenditure of time on the other hand. 
