124 A NEW METHOD OF ESTIMATING STREAM-FLOW 
This formula is identical with that of Professor Adolph Meyer, 1 and was devel- 
oped independently, at a later date, than the latter. The formula developed in 
this investigation, converted to the same units as Freeman's, is 
£„ = 0.319 e+0.358e (w-10.8), in which (B) 
(±0.037)(±0.036) 
e = e a — e d , and e a = Saturation vapor-pressure corresponding to the temperature of the 
air, in inches of mercury; 
e d = Saturation vapor-pressure corresponding to the dew-point temperature, in inches 
of mercury; 
w = average velocity of wind in miles per hour for winds above 10.8 miles per hour; 
that is, the expression 0.358 (w— 10.8) enters only for wind above 10.8 m.p.h. 
The above two formulas differ from each other in three respects, viz, in the 
manner of expressing the wind-term, in the saturation vapor-pressure difference, 
and in the derived proportionality constants. These three differences to some 
extent offset one another, as will be shown later in comparing the aggregate evapo- 
ration computed from them on Lake Michigan-Huron. The formulas are shown 
graphically in figure A. A comparison of them is given in the following paragraphs. 
(a) If there is no error in Assumption No. 5 (page 10), (V — v) = (e a — e d ), and 
the two equations are directly comparable. For a zero wind, the evaporation 
computed by equation (A) is (0.5 — 0.319 = ) 0.181e greater than that computed by 
/0 319 \ 
equation (B). This difference is 4.9 times the probable error of 0.319 ( n „ 7 =49. ). 
Assuming that no systematic or constant errors affect the results, i.e., that the 
probable error ±0.037 represents the true inaccuracy in the constant 0.319, the con- 
stant 0.5 in equation (A) is certainly too large to represent the truth. 
(6) For a wind velocity of 10.8 miles per hour, assuming no error in Assumption 
No. 5, the evaporation computed by equation (A) is (1.04 — 0.319 = )0.721e larger 
than that computed by equation (B). This difference is 19.5 times the probable 
/0.721 \ 
error of 0.319 (^^ = 19.5). Assuming that no systematic or constant errors 
affect the results, the evaporation computed by equation (A) for a wind velocity 
of 10.8 m.p.h. is certainly too large. 
(c) For a wind velocity of 21 miles per hour, assuming no error in Assumption 
No. 5, the evaporation computed by equation (A) is (1.55 — 3.97 = )2.42e smaller 
than that computed by equation (B). Neglecting the entanglement between the 
two terms in the right-hand member of equation (B) when the wind velocity is 
greater than 10.8 m.p.h., the probable error of 3.97 is about ±0.37. The difference 
2.42 is, therefore, 6.5 times this probable error and, if no systematic or constant 
errors affect the results, the evaporation computed by equation (A) for a 21-mile 
wind is certainly too small. 
(d) The above paragraphs, (a), (6) and (c) contain strong indications — proofs — 
that the Freeman or Meyer formula, developed from small-scale apparatus, does 
not represent the true laws of evaporation from a natural body of water. This 
may be indicated in another way. Consider the evaporation formula developed in 
Solution V 2 from observations on Lake Michigan-Huron. This formula is (Tables 
30 and 31). 
1 Trans. A. S. C. E., 1915, p. 1071. 
