118 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
in the reduction from 8 to 6.5, and moreover that analysis showed even 6.5 to be 
too large. 
CONSTANT PART OF RUN-OFF INTO LAKE SUPERIOR 
The original value of the constant part of the run-off into Lake Superior as 
estimated on page 19 at 0.004 foot of depth on the lake area per day was never 
revised in the manner indicated for Lake Michigan-Huron. The equivalent of 
0.004 foot of depth per day on Lake Superior is 41,400 cubic feet per second. 
ENTANGLEMENT BETWEEN CONSTANT PART OF RUN-OFF AND EVAPORATION 
The ideal method of evaluating the constant part of the run-off into the lake 
would be to determine it directly from the least-square computations, instead of by 
the roundabout way adopted. This was tried. The observation equation was 
written in the form of equation (28) except that the constant part of the run-off, 
I e , was not included in the /-term, but was written in as (/. = ) 10 R and inserted 
in the equation just before the rjii — term. In this case R = ttt I c = the constant 
part of the run-off into the lake in — day, was to be determined from the least- 
square computations by trial in the same manner as, and simultaneously with, 
Ri, R 2 , R 3 , . . . R ( . The multiplication of R by 10 merely served to make the 
coefficient of R in the observation equations about the same numerical size as the 
other coefficients as a device to facilitate the computations. 
Many attempts to determine R, and from it I c , in the manner indicated proved 
futile for the reason, which gradually emerged from the computations, that the 
entanglement between R and the evaporation constants E\ and E 2 is very great, 
especially with the former. Because of the entanglement, the derived values of all 
three constants, E x , E 2 , and R suffered. It was of primary importance to evaluate 
Ex and E 2 , with as much accuracy as possible, and it appeared that by dropping 10 R 
from the observation equations and putting it into the absolute term in the manner 
already described, the accuracy of determination of these two constants would be 
greatly increased. This action was later justified, and the conclusion corroborated 
that to determine R from the least-square computations was impossible. 
EFFECT OF VARIABLE PART OF RUN-OFF ON DERIVED VALUES OF E, AND £ 2 
As stated above it was of primary importance to fix the values of £\ and E 2 
with the greatest accuracy possible. The inclusion or exclusion of any element in 
the problem was justifiable on that basis. The rejection of an element was par- 
ticularly justifiable, if its inclusion actually decreased that accuracy. On this 
latter basis the constant part of the run-off was determined in the direct manner 
adopted. 
The variable part of the run-off, which has already been shown to have been 
indeterminable, apparently affected the evaporation constants but little. This 
Value 
of— 
Solution V\ 
Solution V 2 
Difference 
Vi-Vt 
Solution 
Solution 
BB % 
Difference 
BBi-BB 2 
Ei 
E 2 
E, 
+0.493*0.035 
+0.466* .065 
+0.448*0.034 
+ .367* .063 
+0.045 
+ .099 
-0.051*0.059 
+ .721* .155 
+ .653* .261 
-0.045*0.059 
+ .925* .153 
+ .803* .264 
-0.006 
- .204 
- .150 
