APPENDIX TO PART I 
ACCURACY OF COMPUTED EVAPORATION, AND COMPARISON OF FORMULA 
DEVELOPED IN THIS INVESTIGATION WITH OTHERS 
ACCURACY OF COMPUTED EVAPORATION 
What is the accuracy with which the evaporation may be computed on any 
day by use of the formula developed in this investigation? The final formula 
adopted as being the best obtainable is (22) or (23), page 82. Consider the latter, 
in which the evaporation is expressed in units of 0.01 inch of depth per day. The 
value of the constant E x is +0.319 and its probable error is ±0.037. The probable 
error is a measure of the accuracy which is the best that can be obtained, provided 
the errors in the derived constants are all accidental in character. Assuming, for 
the moment, that the errors are all accidental in nature, it is an even chance that 
the actual error in the constant E x is greater or less than its computed probable 
error as shown. That is, the chances are even for and against the proposition that 
the true value of E, lies within 0.319-0.037 and 0.319+0.037. In other words there 
is one chance in two that the value +0.319 is correct within about one-ninth of itself 
f ' Q = -^ ). On this basis the conclusion is that the computed evaporation 
constant Ei is subject to an error which stands 1 chance in 2 of being less than 11.6 
per cent (^- = 0.116 j. Inasmuch as there is, however, evidence of systematic 
error (see page 85, etc.) allowance should be made for this fact. Just how much 
the probable error should be increased to make allowance for the systematic errors 
is a matter difficult, if not impossible, to determine exactly, hence the error in £\ 
will henceforth be discussed as if it were the same as that represented by its prob- 
able error, with the understanding that the accuracy so indicated is probably too 
high. On any day, therefore, on which the wind velocity is less than 10.8 mile? 
per hour, assuming no systematic or constant errors present, and no errors in the 
observed saturation deficit, the computed evaporation stands 1 chance in 2 of 
being in error by less than 11.6 per cent. 
Proceeding in the same manner with reference to the constant E*, its value is 
+ 1.49 and its probable error is ±0.150. Hence, assuming no constant or system- 
atic errors present, the chances are 1 in 2 that the value +1.49 is correct within 
one-tenth of itself ( ' Q = ^r J ; or, stated in a different way, on the above basis 
the computed evaporation constant E 2 is subject to an error which stands 1 chance 
in 2 of being less than 10 per cent as large as E%. As the effect of the systematic 
errors on this probable error is unknown, ± 10 per cent is probably an understate- 
ment of the true error of E 2 . 
It is interesting to note that the accuracy with which the evaporation curve 
for winds above 10.8 miles per hour has been determined is greater than is that for 
winds less than 10.8 miles per hour. Suppose the following inquiry were made: 
What is the error in the computed evaporation when a wind is blowing at the rate 
of 30 miles per hour, as measured by the Weather Bureau anemometers, and the 
saturation deficit is 0.01 inch of mercury? Under these conditions the total com- 
puted evaporation will be at the rate of 0.0717 inch per day, 0.0685 inch, or 96 per 
cent, of which will be contributed by the wind term. If the entanglement between 
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