A NEW EVAPORATION FORMULA 93 
FIRST APPROXIMATION TO MINIMUM WINDS WHICH AFFECT EVAPORATION 
In the seven final least-square solutions for determining evaporation, the 
range in wind velocities tested, below which ventilation is practically ineffectual in 
increasing the rate of evaporation, was from 8.7 miles per hour to 10.8 miles per 
hour, corresponding to values of x of from 2.1 to 2.G, respectively. The questions 
might well be asked: Why stop at these limits? Why not test other values without 
or within these limits? 
Three considerations led to confining the analyses within the limits indicated 
and to omit testing out other values within those limits. The first was the direct 
evidence from Solution V 2 , and its predecessors, the second the indirect evidence 
from both Solutions V 2 and BB 2 , and the third was the economics of the problem. 
The discussion of these three considerations follow. 
In Solution V 2 all wind velocities were used, and the wind term was written in 
(w — 240 \ 
the form of a difference, i.e. ( — inn J, because that form lessened the numerical 
work and also tended to give a better determination of the constants. As men- 
tioned in (c) page 92, w here applies to all wind velocities, and is not limited 
to higher winds only, as defined on page 9. The value, 240 miles, for the mean 
daily wind travel, was determined statistically to be about right for the two areas 
concerned. In the Solution V 2 equation, therefore, the second term is subtractive 
for winds less than 240 miles per day and additive for winds greater than that. 
Using the values of the two derived constants shown in Table 31, for a zero wind — 
a day of perfect calm — the computed evaporation is + 0.448 + 0.367 ( — 2.4) = 
— 0.433 in terms of e. This result is obviously absurd. 
A study of the probable errors of E x and E 2 in connection with this result indicates 
that in order that the evaporation shall be greater than zero for a zero wind, the 
value of E x would have to be increased, and that of E 2 decreased, by somewhat 
more than twice their own respective probable errors. It is highly improbable that 
the derived values of E\_ and E 2 from Solution V2 could be in error by the amounts stated 
as a result of inaccuracies in the absolute term, I. And, on the other hand, it does not 
appear possible that they are that much in error because of errors in Assumption No. 5. 
In other words, in order that the expression shall give positive evaporation at all wind 
velocities, the straight-line formula as in Solution V \, in which all values of the wind 
velocity enter the second term, can not be adopted to represent the facts. 
This evidence (from Solution V 2 , of negative evaporation with zero wind) 
could be interpreted in two ways. First, it could be interpreted as meaning that 
the evaporation curve, plotted with winds as abscissas (Plate 6), is concave upward 
instead of a straight line. Or it could be interpreted as meaning that the evapora- 
tion is inappreciably affected by winds as strong as 10 miles per hour or less. The 
actual evidence against the first interpretation, obtained from previous least-square 
solutions on Lake Michigan-Huron indicated that the exponent of the wind term 
was unity for all wind velocities on that lake. This evidence will be presented 
later in discussing the wind exponent. 1 The evidence in support of the second pos- 
sible interpretation will be presented in connection with the discussion of the 
second consideration mentioned in the third preceding paragraph which led to the 
range of winds used. 2 
1 See page 99. 2 See page 96. 
