A NEW EVAPORATION FORMULA 125 
E w =+0A4Se +0.367 
(±0.034)(±0.063)|_\100 
^"24 

It is based upon 778 observation equations covering 842 days. Converted to the 
same units as in equations (A) and (B), it is 
E w = +0.448e +0.0881e(>- 10) (D) 
(±0.034) (±0.015) 
in which w has the same meaning as in (A) and e the same meaning as in (/?). 
This equation is also shown plotted on figure A. Equation (D) is of the same form as 
equation (A). In its derivation all wind velocities were used. It is directly comparable 
with the Freeman and Meyer formula, if there are no errors in Assumption No. 5. 
The impossibility of representing the variation in evaporation by this form of expres- 
sion has already been pointed out (page 93, etc.). It proves that the assumption that 
evaporation is affected by all wind velocities on the Great Lakes — wind velocities 
as measured at the Weather Bureau Stations — is not true. Moreover, it shows that 
if this assumption be made, as in the Freeman and Meyer formulas, the rate of increase 
of evaporation with increasing wind velocity is greater than that represented by the 
Freeman and Meyer formula. In support of this last statement, note that the con- 
stant representing the slope of the curve (D) is (0.0881 — 0.05 = ) 0.0381 greater than 
(0 0381 
' ... 
.Ulol 
, strong indication in itself that the slope of the Freeman curve is too small. 
Additional proof that that slope is too small is seen in the large increase in the 
slope between Solutions V t and V t , where the increase was from +0.367 ± 0.063 
to +0.661 ±0.085 (Table 31), an increase due solely to the assumption that, 
for small winds, evaporation is practically independent of wind velocity. 
(e) The two equations, (A) and (B), give the same evaporation at a wind 
velocity of about 13.1 m.p.h., where the curves intersect. For winds below this 
velocity, equation (A) gives results which are certainly too high, and for winds 
above that, certainly too low as judged by the probable errors of the constants in 
equation (B), the best available criteria. The area between these curves to the 
left of this point of intersection is about 35 per cent greater than the area to the 
right of that point up to winds of 21 m.p.h. This means that if, over a long interval 
of time — say a year — there are as many winds between 13.1 and 21 m.p.h. as there 
are below 13.1 m.p.h. the overall evaporation computed from (A) will be 35 per 
cent greater than that computed from (B). The upper limit of 21 m.p.h. is approxi- 
mately the maximum average wind velocity which entered into the observations 
on which the constants in equation (B) are based. The average referred to is that 
computed from the ten stations near Lake Michigan-Huron, or from the five sta- 
tions near Lake Superior (Tables 1 and 2) . With an average based on ten stations — 
an average velocity assumed to be representative of the whole lake area — the maxi- 
mum wind at a single station might be much above, or the minimum wind much be- 
low, 21 miles per hour. When the average daily wind velocity exceeded this amount, 
the observations were rejected because, as noted elsewhere, the observed change of 
elevation of the water surface on the day in question was abnormal and due to the 
first oscillation of a new seiche affecting the gage record at the station, or that it was 
abnormal because of extremely rapid and irregular changes in barometric gradients 
over the lake, which departed widely from the conditions postulated in the approxi- 
