A NEW EVAPORATION FORMULA 127 
Law. These formulas are shown below, together with the one developed in this 
investigation, the evaporation being expressed in millimeters per hour. 
Abassia: 
E, mm/h.r = 0.0122 (e„-e d ) +0.00029 (e a -e d ) v (E) 
Fitzgerald : 
E, mm/hr = 0.0166 (e w -e d ) +0.000783 (e*-e d ) v (F) 
Carpenter : 
E, mm/hr = 0.0161 (e„-e d ) +0.0000895 (e.-e„) v (G) 
Stelling: 
E, mm/hr = 0.0351 (e.-c) +0.00044 (e v -e d ) v (77) 
Mean, 
E, mm/hr = 0.0200 (e„-e d ) +0.000401 (e„-c d ) v 
This investigation: 
E, mm/hr = 0.0133 (e a -e d ) +0.0334 (e a -e d ) (w-4.84) (7) 
(±0.00154) ( = 0.00336) 
1 „ ' 
(Enters only for v 5; 4.84) 
The saturation vapor-pressures corresponding to the surface-water tempera- 
ture, to the dew-point temperature, and to the air temperature are e„, e d and e a , 
respectively, and are expressed in millimeters of mercury. The wind velocity, v, 
is in meters per second. The five equations are shown graphically in Figure B. 
The chief point of difference between (7) and (E), (F), (G) and (77) is in the wind 
term. 
Comparing the formulas in detail, the mean coefficient of (e„— e d ), +0.0200, is 
larger than the coefficient of (e a — e d ) in (7) by 0.0067, an amount 4.4 times the 
probable error of the coefficient of the latter ( -—^-=.=4.4 ). Similarly, the 
coefficient of (e a — e d ) is about twice its own probable error smaller than the corre- 
sponding coefficients derived by Fitzgerald and Carpenter. It differs from the 
Abassia value, however, by an amount less than its own probable error. 
The coefficient of (e a -e d )(v-4.84) in (I), +0.0334^0.00336, is 83.3 times 
larger than the mean coefficient of (e„ — e d )v in equations (E), (F), (G), and (77), 
+0.000401. The difference between these values is ( — — n ormfi r'^ 
times the probable error, ±0.00336. Neglecting errors in Assumption No. 5, and 
the effects of systematic and constant errors, this is a strong indication — proof — 
that the wind terms in equations (7?), (F), (G) and (77) are too small to represent 
the true rate of increase of evaporation on a natural body of water with increasing 
wind velocity for winds above 4.84 meters per second. For small winds — those 
less than 4.84 meters per second — the differences are not nearly so serious, except 
in the case of the Stelling formula. 
Using a value of (e v —e d ), or (e a —e d ), of 8.85 mm. and a value of v of 10 
meters/sec, the rate of evaporation as computed from equations (E) to (77) by 
Professor Bigelow, are compared below with that computed from equation (7). 
Abassia, E, mm/hour = 0.1080+0.0257 = 0.1337 
Fitzgerald, E, mm/hour = 0.1469 +0.0693 = 0.2162 
