A NEW EVAPORATION FORMULA 129 
Carpenter, E, mm, hour = 0.1425+0.0079 = 0.1504 
Stalling, E, mm/hour = 0.3106 + 0.0389 = 0.3495 
Mean of above four, E, mm/hour = 0.1770+0.0354 = 0.2124 
This investigation, E, mm/hour = 0.1177 + 1.5264 = 1.6441 
( = 0.0136) ( = 0.153) 
Here, as with the comparison of the general formulas, the difference between 
the total evaporation, 1.6441 m.m./hour and the average total from the other four 
formulas, 0.2124 m.m./hour, is much too great to be accounted for by the probable 
errors. 
COMPARISON WITH FORMULA PROPOSED BY MARVIN 
The evaporation formula proposed by Marvin 1 is 
* = £(e.+e.-2«,) / (e) / 00 (J) 
The form of this formula is in substantial agreement with the one developed in 
this investigation (B). In the latter, the effect of barometric pressure on evapora- 
tion, denoted by B in equation (J), has been thrown into the constants £\ and E 2 
because the effect of the variation in barometric pressure on evaporation is small in 
comparison with other, unavoidable errors. Also, by Assumption No. 5, e. — e a in 
equation (J). On the basis of the two preceding sentences, we might rewrite (J) 
as follows: 
f r E(e a -e d )f(e)f(v) (K) 
Equations (K) and (B) are the same in form, neglecting errors in Assumption 
No. 5, and the variation in the effect of barometric pressure on evaporation. In 
this investigation the functions /(e) f(v) have been determined in the manner set 
forth in detail in the text, from the actual observations of real evaporation on a 
natural lake under natural conditions. 
CONCLUSIONS ON COMPARISON OF EVAPORATION FORMULAS 
The chief difference between the evaporation formula developed in this inves- 
tigation and the formulas based upon small scale apparatus lies in the wind term. 
The rate of increase of evaporation from the natural lake surface with increasing 
wind velocity, as established in this investigation, is many times greater than the 
corresponding rate from evaporation pans, as established in other studies. Two 
causes of the difference are apparent. In the first place, the wind velocity used in 
the establishment of the formula in this investigation is observed at an elevation of 
about 100 feet above the water surface. This, in itself, would tend to make the 
derived wind coefficient larger than it would be if the observations of wind velocity 
had been taken at a lower elevation, as in most evaporation pan experiments. In 
the second place, the water-surface exposed to evaporation at high winds is very 
much greater on a large, natural body of water, such as on any one of the Great 
Lakes, than it is in evaporation pans. Consider a natural lake under the influence 
of a wind of increasing velocity, beginning at zero. The water surface, from a plane 
1 A Proposed New Formula for Evaporation, by C. F. Marvin, Monthly Weather Review, vol. xxxvii, No. 2, 
page 57 (Feb. 1909). 
