A NEW EVAPORATION FORMULA 
81 
least-square solutions made prior to Publication No. 317 also gave information 
on these two subjects, and gradually served to point the way to the best form for 
the evaporation formula. On the subject of evaporation only, 7 le:ist -square 
solutions were made, each having its observation equation of the form of equation 
(1), or slight modifications thereof, and each being based upon 28 months of daily 
observations on one or the other of Lakes Michigan-Huron or Superior. The 
two final solutions of the 7 in the evaporation series, which served to fix the values 
of the unknowns E 1 and E I} and to establish the constant 2.6 in equation (1), 
were designated as Solution V t on Lake Michigan-Huron, and Solution BB t on 
Lake Superior. 
The normal equations for Solution V h formed from the list of 755 observation 
equations shown in Table 24, are as follows: 
+240,627 £, + 17,336 £ 2 -85,953 = 0\ 
(19) 
+ 17,336 £, + 10,681 £ 2 -18,176 = 
The solution of the final normal equations for Solution V h (19), gives the 
following values for the unknowns: 
E 1 = +0.266 ±0.031 £ 2 = +1.27 ±0.148 
The probable errors shown were computed rigorously from the normal equa- 
tions, (19), and from the residuals, v, of the 755 observation equations of Solution 
V*. 
The observation equations for Solution BB t , Lake Superior, similar to those 
for Solution V h Lake Michigan-Huron, will not be presented for want of space, 
and because they contributed very little, as will be seen, to the final results. 
The normal equations for Solution BB t) formed from the 745 observation 
equations in that solution, are as follows: 
+ 193,312 £, + 15,122 £ 2 +12,182 = 0-| 
)i 
(20) 
+ 15,122 £,+ 9,500 E 2 - 8,736 = OJ 
The solution of the final normal equations for Solution BB t , (20), gives the 
following values for the unknowns: 
£,= -0.154 = 0.052 £ 2 = +1.16 = 0.234 
The probable errors shown were computed rigorously from the normal equa- 
tions, (20), and from the residuals of the 754 observation equations. 
PRINCIPAL FACTS FROM THE TWO FINAL EVAPORATION SOLUTIONS 
The principal facts from Solutions V 6 and BB t are summarized in Table 25. 
Table 25 — Principal facts from the two final evaporation solutions 
Solution y 5 
Solution BB t 
M ichigan-Huron 
Superior 
818 
847 
755 
754 
+0.266 
-0.154 
±0.031 
±0.052 
+ 1.27 
+ 1.16 
±0.148 
±0.234 
2.6 
2.6 
±0.014 ft. 
±0.021 ft. 
Lake on which observations were made 
No. of days of observation used in Solution 
No. of observation equations 
Computed value of i?, 
Computed probable error of E\ 
Computed value of E 2 
Computed probable error of £2 
Assumed value of a: 
Probable error of single observation of rise of water surface in one 
day 
