94 A NEW METHOD OF ESTIMATING STREAM-FLOW 
The evidence from Solution V, noted in the second preceding paragraph is very 
strong. Note that the solution contained 778 observation equations, very much 
the same ones as shown in Table 24. Other values of E x and E, from solutions 
containing fewer observations on both Lakes Michigan-Huron and Superior, and 
with the straight-line form of equation, as in Solution V,, gave negative evaporation 
at zero winds, thus corroborating the evidence from Solution V t . 
Before presenting the direct evidence from Solutions V, and BB, as to the 
point at which the wind velocity begins appreciably to affect the rate of evapora- 
tion, the results of Solution BB, will be discussed further. From earlier solutions 
than BB, on Lake Superior, faint evidence was found of a possible curvature in the 
evaporation curve for low wind velocities on that lake. That is, on that lake and 
contrary to the findings on Lake Michigan-Huron, faint evidence was obtained 
that the exponent of the wind term is greater than unity for low winds. This 
evidence will be given in detail later in discussing the wind exponent. 1 With that 
evidence as a basis, Solution BB, was set up to make a thorough test, based upon a 
large number of observations. The results are shown in Table 31 and in the 
evaporation curve shown on Plate 6 computed by substituting those constants in 
the general equation shown in Table 30 for various winds. (This computation 
occurs in columns 1 to 6, Table 32.) This parabolic curve is typical of several 
others obtained from shorter solutions. It shows a minimum — and negative — 
evaporation for a wind velocity of about 7.5 miles per hour, and an increasing 
evaporation for decreasing winds, both of which conditions are contrary to our 
general knowledge of the subject. 
Having obtained the strong evidence from Solution V, and its predecessors 
that the evaporation curve is not a straight line for all wind velocities, and from 
Solution BB, that it is not represented by an equation of the second degree for 
winds less than 10 miles per hour, the residuals of those two solutions were studied 
for the purpose of estimating the probable shape of the evaporation curve. These 
studies furnished the second consideration mentioned on page 93 which led to 
limiting the range of wind velocities tested to from 8.7 to 10.8 miles per hour. The 
results of these studies are presented in tabular form in Tables 32 and 33, and are 
plotted on the upper part of Plate 6 in the first three curves mentioned in the legend. 
Referring first to Table 32, the first six columns merely represent the computa- 
tion of the total evaporation in terms of e from the Solution BB, equation for 
various assumed wind velocities. In the seventh column is shown a correction, 
which is stated to be the negative of the mean v divided by the mean e. The mean 
v and the mean e for each wind velocity is the mean of all such values for that wind 
velocity which occurred in the 759 observation equations used in Solution BB,. 
The mean v for any wind velocity with the sign changed, divided by the mean e for 
that wind velocity, gives the correction to the computed evaporation in terms of e 
to get the true evaporation at that wind velocity in terms of e. The corrected 
evaporation is shown in column 8. This corrected evaporation in terms of e can 
now be plotted with evaporation as ordinates and wind velocity as abscissa?, and 
the resulting curve will be an approximation to the true evaporation curve as 
determinable from observations on that lake. Inasmuch as this curve was very 
irregular, the observations were combined into larger groups as shown in the last 
two columns. The values in the last column but one were not obtained from the 
1 See page 99 . 
