A NEW EVAPORATION FORMULA 51 
Applying the weights 1.9, 2.9 and 5.1 to the corrected elevations at the three 
gages, as shown in Tables Nos. 20 to 22, respectively, there is obtained the weighted 
mean elevation of the whole surface of Lake Michigan-Huron. This weighted 
mean elevation is shown in column 3 of Table 23, headed "Observed elevation 
corrected for wind and barometric effects." Usually the corrected elevations 
at all three gages were obtainable and usable in thus evaluating the elevation 
of the mean surface of the whole lake. At such times the sum of the weights is 
9.9. On some days the criterion causes rejections to be made in the corrected 
elevation at one or more gages. In such instances the evaluation of the mean 
elevation of the whole lake surface for the day was made from the retained cor- 
rected elevations at the two or less gages. In the specific instance, August 23, 
1910, referred to previously, the mean corrected elevation not being determinable, 
that fact is noted by a dash enclosed in parentheses. 
In the preceding paragraph has been illustrated Step (d), page 33, in the 
computation of I u The final step, (e), in the computation, consists in taking 
the differences from day to day between the weighted mean elevation of the whole 
lake surface as computed for each day. This is shown in column 4, Table 23, 
headed "Rise of mean lake surface." Thus from August 24 to August 25, 1910, 
the mean surface of the whole lake rose 0.060 foot. 
COMPUTATION OF ABSOLUTE TERM. /, IN OBSERVATION EQUATION (1), FOR LAKE 
MICHIGAN-HURON 
The definition of I is given on page 9. Its computation for all of the days 
of observation on Lake Michigan-Huron used in this investigation is shown in 
the fourth to tenth columns, inclusive, of Table 23. In that table, beginning at 
the left, the second column shows the observed elevation of the lake surface in 
feet above mean sea-level at New York. This is taken as the arithmetic mean 
of the observed levels at Milwaukee, Harbor Beach and Mackinaw. 
In the third column are listed the observed elevations corrected for wind and 
barometric effects. The fourth column shows the rise of the mean lake surface, 
the 1 1 of equation (1). The fifth, sixth, seventh and eighth columns show the 
corrections for, respectively, inflow from Lake Superior {—It), outflow to Lake 
Erie (+/«), rainfall on the lake (— 7 2 ), and run-off into the lake (— I e ). The 
ninth column shows the sum of the separate corrections, i.e., —/,+/« — 7 2 —/ e . 
The tenth column shows the "net rise" of the lake surface, the I, or absolute 
term, of equation (1). This is the sum of the fourth and ninth columns. It 
will be observed that some of the values of I represent the combination of two 
or more days, and other values, marked with a star (*), are indicated as rejected. 
The values indicated as rejected were detected by a definite numerical cri- 
terion, the final value of which gradually emerged from the series of least-square 
solutions which served to fix the laws of evaporation as established in this investi- 
gation. On lake Michigan-Huron, the last such solution but one, Solution V A , 
had for a probable error of a single change in elevation ±0.016 foot. Hence 
in making Solution V B , every date which showed a residual larger than five times 
the probable error, or (5 X =*= 0.016 = ) =*= 0.080 foot, was rejected. By this rule less 
than one equation per thousand would have been rejected if the causes of the 
abnormal residuals had been all accidental in character. In Solution V h the 
final solution on Lake Michigan-Huron, the total number of rejected equations 
was 39 out of a possible 849. This is at the rate of 46 per thousand. The large 
