A NEW EVAPORATION FORMULA 85 
In order better to compare the computed evaporation and the absolute term, 
J, the accumulated sums of these quantities have been obtained, and are shown 
in the last two columns of Table 23. This accumulated sum begins anew each 
year; thus on October 31, 1913, the accumulated sum of the computed evapor- 
ation since May 2, 1913, amounted to 1.059 foot of depth on Lake Michigan-Huron. 
The corresponding accumulated sum of the absolute terms, 7, or net rises, was 
— 1.087 foot, which is the directly observed fall — that is, negative rise — of the 
mean lake surface in that time interval, corrected for the various influences. 
On Plate 5 is shown the comparison of the accumulated sums by months for the 
five years, and for the mean of the five years 1909-1913. 
On Plate 5 it may be observed that in each year the computed rate of evapor- 
ation is larger in May and June, and smaller in September and October, than the 
actual rate of net fall of the lake surface, whereas in July and August the two rates 
are about the same. It is believed that this divergence of the two accumulation 
curves at the beginning of the season, and their subsequent convergences at the 
end of it, is due to principally the variable part of the run-off into the lake, at- 
tention to which has been called previously, with the statement that the only 
method devised for its evaluation failed. By reference to Table 23, it is easy to 
see that if the run-off had been taken larger than 6 (i.e., 0.006 foot of depth per 
day) in May and June, and smaller than that in September and October, the 
accumulation curves would have approached each other more closely throughout 
their extent. It is knowm qualitatively that the run-off is larger in May and 
June than it is in September and October, but it is not known, and could not be 
determined, quantitatively, how much. The value 0.006 foot of depth per day 
for the run-off is about right for the constant part of the run-off into the lake, or 
the run-off when the ground water is at its average level and (rainfall on land) 
minus (evaporation from land) minus (run-off from land) has been zero for a 
long time. This was obtained by revising the first approximate value of 0.008 
foot, obtained as described on pages 16 to 19, by least-square computations in a 
manner yet to be described. Hence, it is reasonably certain that if the variable 
part of the run-off could have been properly taken into account, the accumulation 
curves on Plate 5 would have been closer together throughout their lengths, and 
therefore their differences can not all be charged against systematic errors in the 
computed evaporation, but must be sought, rather, in the variable part of the 
run-off. This will become clearer from an analysis of the residuals, which follows. 
RESIDUALS FROM SOLUTION K 5 
The comparison between the computed evaporation and the directly observed 
fall in the lake surface will now be given in the form of differences; that is, in the 
form of the residuals, v, a positive residual, meaning that the computed fall of the 
lake surface due to evaporation is larger than the directly observed fall thereof, 
corrected for the various influences. 
The mean residuals shown in Table 27 w T ere computed from the list in Table 28. 
Each mean residual is the algebraic sum of the residuals divided by the number of 
residuals in the period involved, except in the last column but one, where they are 
the mean of the mean residuals in the 5 preceding columns, and except in the case 
of the mean annual v, which is the mean of the mean monthly v's in the 6 lines 
above it. The probable error of each mean v, monthly, annual, or for the whole 
