92 A NEW METHOD OF ESTIMATING STREAM-FLOW 
more days and more observation equations, as shown in Table 31. In other words, 
after the completion of Solution V,, its derived probable error, ±0.016 foot, indi- 
cated that certain additional equations should be combined to form one equation, 
or that certain equations should be rejected, according to the criteria used for 
combinations and rejections stated on pages 51 and 73. Solution V h the 
successor to Solution V,, contained these changes, but in other respects they were 
identical. 
(6) Solution V 3 differed from Solution V, in respect to the same type of difference 
as mentioned in (a) between Solutions V, and V h and also in the use of the value 
2.1 for x in place of 2.6. That is, Solution V 3 served principally to test out the 
assumption that the minimum wind velocity which affects the evaporation is 210 
miles per day, instead of 260. 
(c) Solution V 2 differed from V 3 in the respects stated in (a) and (6) and in the 
additional respect that all wind velocities were used. That is, Solution V 2 served 
principally to test out the assumption that the evaporation was affected by all wind 
velocities, both above and below an assumed mean wind velocity of 240 miles per 
day, or 10 miles per hour. 
(d) The results from Solution BB, have already been presented, culminating 
on page 90. The form of equation is identical with that of Solution Vt. 
(e) Solution BB 3 differed from Solution BB, in the same manner as Solution 
V, differed from Solution V,, as mentioned in (6), above. 
(/) Solution BB 2 differed from Solution BB, in the same manner that Solution 
Vi differed from Solution V 3 , as stated in (c), above, and also in the fact that it 
contained an additional term el y^— 2.4J IE,, which was inserted for all days 
on which the wind velocity was less than 10 miles per hour, or 240 miles per day. 
Solution BB 2 served the same purpose as Solution V 2 , and in addition, served to 
test out the assumption that the evaporation curve, for winds below 10 m.p.h., is 
in the form of a parabola. 
The results from the seven least-square solutions are concisely shown in Table 
31 in the number of observation equations used in each solution, in the derived 
values of the constants, in their probable errors, in the probable error of a single 
observation, in the mean v 2 , and in the sum of the squares of the residuals. On 
Lake Michigan-Huron, Solution V t was adopted as being nearest the truth as shown 
by the sum of the squares of the residuals being a minimum, the probable errors of 
the constants being a minimum, the probable error of a single observation being a 
minimum, and the mean v 1 being a minimum. On Lake Superior, in so far as the 
sum of the squares of the residuals is concerned — the principal single test — the 
choice is in favor of Solution BB,. But in Solution BB,, the value of Ev is a much 
smaller negative value than in Solution BB 3 , and the wind coefficient, E 2 , is nearer 
the value derived in Solution V t . These two improvements were judged to out- 
weigh the slight deterioration of Solution BB, over Solution BB 3 as shown by the 
sum of the squares of the residuals, and Solution BB, was adopted as best repre- 
senting the facts on Lake Superior. 
The two adopted solutions, V t and BB,, both contain the assumption that the 
evaporation is little affected by winds less than 260 miles per day. They serve to 
establish the value 2.6 as the most probable value of x in the expression ( T7u\~ x )- 
