A NEW EVAPORATION FORMULA 9 
w = average travel of the wind, for winds greater than x, in miles per 2-1-hours, over the 
whole lake surface for the two days ending at midnight at the end of the date to which 
the observation equation refers, the mean being taken without any regard to the 
direction of the wind. 
x=that value of the wind travel, w, in units of 100 miles per day, below which the evapora- 
tion from the lake surface is inappreciably affected by the wind. 
E2 = that part of the evaporation which is proportional to the product of the vapor-pressure 
potential and the wind velocity, for winds greater than x. 
-f 7 = + I1—I3 + 7 4 — 7 2 — 1 £ = that part of the directly observed rise in the mean lake surface 
which is unaccounted for in terms of 7 3 , 7 4 , 7 2 and Ic In other words 7 is that part of 
the directly observed rise which is to be accounted for as much as possible by the 
evaporation from the lake surface. 
+7i = (weighted mean elevation of the water surface of the lake on the current day, from 
readings on all of the available, reliable gages, corrected for wind and barometric 
effects) minus (weighted mean elevation of the water surface of the lake on the preceding 
day, from readings on all of the available, reliable gages, corrected for wind and 
barometric effects). In other words +7i is the rise in the mean surface of the whole 
lake from the preceding to the current day, the elevation of the mean surface on each 
day being determined as accurately as possible by applying corrections for the effects 
of winds and barometric pressures. Unit = 0.001 foot. 
J, = Computed rise of the lake surface due to inflow into the lake from the next lake above in 
the chain of lakes. Unit = 0.001 foot. 
I t = Computed fall of the lake surface due to outflow from the lake into the next lake below 
in the chain of lakes. Unit = 0.001 foot. 
It = Computed rise of lake surface, noon to noon, due to rainfall on the lake surface. It is 
assumed to be the mean between the rise as computed from the rainfall on the preceding 
day, and the rise as computed from the rainfall on the current day. Unit = 0.001 foot. 
Ic = Estimated constant part of the run-off into the lake in one day. It is the run-off when 
the ground-water is at its average level and the quantity (rainfall on land) minus 
(estimated evaporation from land) minus (estimated run-off) has been zero for a long 
time. Unit = 0.001 foot. 
In equation (1), only positive values of the expression in brackets were used. 
The full explanation for this will be fully stated in appropriate places. 
The right-hand member of equation (1), v, is a residual. It represents the 
discrepancy between the observed rise of the lake surface corrected for the various 
influences, +7, and the computed fall of the lake surface due to evaporation, 
+eE l +e 
[(m~ x \ 
E 2 . If the agreement between the theory and the facts were 
perfect, and if there were no errors in the observations and computations, the 
residuals would all be zero. The closer this agreement and the smaller the errors of 
the kind stated, the smaller the v's tend to become, and the more closely they 
approach the law of distribution of accidental errors. 
The least-square solutions serve to determine the most probable values of the 
two unknowns Ei and E 2 directly, and of the third unknown, x, indirectly. 
The division of the wind velocity, w, by 100 was made simply for the purpose 
of making the average coefficient of E 2 the same numerical size as the average 
coefficient of E\ and the absolute term, 7. Such approximate equality facilitates 
the least-square computation by providing certain checks against numerical error. 
The use of equation (1) involves an important assumption which will be stated 
at this point, and designated as Assumption No. 5. (For the other four principal 
