A NEW EVAPORATION FORMULA 83 
The probable error of each constant in the last equation is shown in paren- 
theses immediately beneath the constant, and is obtained by multiplying the 
probable error in (21) by the same conversion factor used in converting (22) into 
(23), viz, 6/5. 
Equation (22) (or (23)) is the final evaporation formula as determined in this 
investigation of the laws of evaporation. It is based upon a total of 1,509 obser- 
vations on two independent lakes, Michigan-Huron and Superior. It is based 
upon the facts drawn from the large scale of nature, and under natural conditions, 
as contrasted with the numerous evaporation equations based upon observations 
on evaporation pans of a few square inches or a few square feet in area. This 
equation should enable one to compute the evaporation from any free, open 
surface of water — from any reservoir, lake, river, bay, gulf — anywhere in the 
world from observations of the meteorological elements of air temperature, vapor- 
pressure and wind velocity as observed at the regular U. S. Weather Bureau 
Stations. The uncertainty which accompanies the use of the evaporation-pan 
formulas in estimating the evaporation on the large scale of nature should not 
exist with the use of equation (22), because it is based directly upon the large 
scale of nature and under natural conditions. The evaporation pan has, in this 
case, been the lake itself. The evaluation of the fluctuation of the elevation of the 
mean surface of the whole lake has been made with sufficient accuracy to segregate 
that part of the outgo which is evaporation, and the quantitative expression by 
which the evaporation can be evaluated has been obtained with a fair degree of 
accuracy. The probable error of Ei is l/9th of itself, ( f .'„ g = ^-^) and of E if 
/0 12^ 1 \ \u.^bo ».o/ 
l/10th of itself \j^=^q) 
In developing equation (22), a two-day interval was involved in each obser- 
vation equation (not counting the combined equations) ; that is, a change in the 
elevation of the water surface from one day to the next was used. In using the 
equation to estimate the evaporation from a water surface on any day, the quan- 
tities e and w to be substituted therein should be the mean values for the day 
only for which the evaporation is wanted. Hence the specific definitions of e and 
w for use in equations (22) and (23) are as follows : 
e is the mean difference for the lake (or reservoir, river, etc.) between (1) the saturation 
vapor-pressure corresponding to the mean air temperature for the day for which the evapo- 
ration is wanted, and (2) the actual, observed mean vapor-pressure for the lake (or reser- 
voir, river, etc.) for that day. The unit in which e is expressed is 0.01 inch of mercury. 
w is the average travel of the wind, in miles per 24-hours, over the whole lake (or 
reservoir, river, etc.) surface for the day for which the evaporation is wanted, the mean 
being taken without any regard to the direction of the wind. 
E w is the total evaporation from the water surface for the day, expressed in units of 
0.001 foot in equation (22), and in units of 0.01 inch in equation (23). 
The second term of the right-hand member of equations (22) and (23), viz, 1.24 
{{m-™)]™ ilM [{m- 2 «)\ 
respectively, enters only for winds greater than 
260 miles per day or 10.8 miles per hour; that is, only plus values of that term are to be used. 
Since the quantities e and w used in deriving equation (22) were obtained 
from meteorological observations as ordinarily made by the U. S. Weather Bureau 
stations surrounding the Great Lakes, in using the formula to evaluate the evapor- 
ation in any locality it is to be understood that observations similarly made are 
