A NEW EVAPORATION FORMULA 117 
the other extreme, the estimated variable part of the run-off was —0.005 foot, 
which decreased the constant part of the run-off into Lake Michigan-Huron to 
0.001 foot. 
The conclusion, that the variable part of the run-off is so small that it can not 
be evaluated by the form of expression adopted, would be affected but little, it is 
believed, by the errors in the estimated evaporation from land, used in computing 
r,, r 2 , r 3 , . . . r 6 . The difference between that estimated evaporation and the 
true evaporation would probably introduce a negligible error into the evaluation 
of Ri, R2, R h . . . Rt, in comparison with other unavoidable errors. 
CONSTANT PART OF RUN-OFF INTO LAKE MICHIGAN-HURON 
The original estimate of the constant part of the run-off into the lake in one 
day, I e = 0.008 foot, page 19, was revised in the following manner. Consider the 
change in storage in the drainage area, represented by the r l — term. It is evident 
that over any long period of time for which the constant part of the run-off has 
been assumed correct, 2(r,)=0. Any variation from zero must be attributable 
largely to errors in the estimated run-off rather than to errors in the estimated 
evaporation, since the former was the more uncertain quantity involved in the 
computation of r u Between two least-square solutions in which the variable part 
of the run-off is held the same, i.e., computed by the same assumed R's, but the 
constant part of the run-off, I c — and that only — is caused to vary, one can get a 
variation in 2(n) and in its mean value 2(ri)/n. where n is the number of observa- 
tions used in the solution. By comparing the change in 2(r : )/n between the two 
solutions with the assumed change in I e in connection with the knowledge that 
2(r,)/n should equal zero, that value of I c may be estimated which will render 
2(r,) zero. This reasoning is believed not to be vitiated even though the assumed 
R's used in the two solutions be so much as 40 per cent from the true values. 
In Solution 7\, containing 169 observation equations of the form of equation 
(28), and in which I e = 8 was used, the value of 2(n)/(169) was +0.75. In Solution 
T 6 , exactly like Solution 7\ except that 7 C = 6.5 was used, the value of 2(r,)/(169) 
was +0.18. That is, the change of assumption of I, from 8.0 to 6.5 changed the 
mean value of r t from +0.75 to +0.18, from which it is seen that the value of 6.0 
for Ic would make the mean r, = 0. This final adopted value of 0.006 foot of depth 
per day on the lake area for the constant part of the run-off into Lake Michigan- 
Huron or, otherwise stated, for the run-off when the ground water is at its average 
level, and the quantity [(rainfall) minus (evaporation from land) minus (run-off)] 
has been zero for a long time, it is believed to be in error by not more than 
±0.0005 foot. The equivalent of 0.006 foot of depth per day on Lake Michigan- 
Huron is 87,900 cubic feet per second. 
The evidence in favor of the reduction from 8 to 6.5 was of four kinds, each 
independent of the others, and only one of the four being internal evidence from 
the least-square computations, in which case it was of different character from the 
type already presented. Each of these four lines of evidence indicated 8 to be too 
large, and after rejecting one of the values, which appeared to have been determined 
from uncertain premises, the mean of the other three values was 6.7. The value 
was arbitrarily reduced to 6.5 to facilitate computations. These four lines of 
evidence need not be given here, for the reasons that the final reduction from 6.5 
to 6.0 involved a more potent method of analysis than any one of the three involved 
