116 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
The derived values of the run-off constants from Solution BB t differ much less 
from the assumed values than was the case in Solution V u Only one derived value, 
Ri, differs by more than 3.5 times its own p.e. from the assumed value. The mean 
difference of all the derived R's from their assumed values is only 2 times their own 
probable errors, as against 4.5 times their own p.e.'s in Solution V u This evidence 
is a strong indication that the assumed R's in Solution BBi are much nearer the 
truth than they were in Solution V h or that the amount of the change in storage 
on the current day, which is delivered to the lake by the end of the following six- 
teenth day, if, during the last 16 days of that 17-day period, the storage in the 
ground does not change, is much nearer 1.44 per cent of such change than 37 per 
cent of it. In fact, the derived run-off constants indicate that —10.6 per cent 
of the change in storage in the ground on any day is delivered to the lake by the 
end of the sixteenth day thereafter, which is an absurdity and an indication that 
even the assumed 1.44 per cent is possibly too large for the Lake Superior drainage 
basin. On the other hand a comparison of the run-off values as finally derived on 
Streams A and B, shown in Table 51, page 195, with the first approximate values 
derived on those streams and used in Solution B B h shows that the correct mean 
Value of — 
Assumed in 
Solution B Bi 
Mean of final 
values derived on 
Streams A and B 
i?i 
R> 
R» 
Rt 
p. ct. 
0.20 
0.40 
0.30 
0.125 
0.050 
0.01125 
1.44 
p. ct. 
0.186 
0.152 
0.124 
0.106 
0.092 
0.080 
1.68 
i? 8 
Total 
value for Streams A and B is 1.68 per cent rather than 1.44 per cent, as shown in 
the accompanying tabulation. The two lines of evidence are contradictory, if the 
assumption is true that the natural underground drainage systems of the two 
regions is substantially the same. 
From another viewpoint, however, it appears that whether the R's be assumed 
in such sizes and relations to each other that the total amount of excess storage on 
a day which is delivered to the lake by the end of the sixteenth day thereafter be 
1.44 per cent or 1.68 per cent of such excess storage, if the rainfall on each day after 
the first of the 17-day period is just equal to the evaporation from land plus the 
run-off, is relatively immaterial. The probability is that in neither case could the 
R's be derived from the observations. This is true because the variable part of the 
estimated run-off with such small R's as were assumed in Solution BBi never 
totaled to as much as 0.001 foot of depth on the lake area. This means that the 
assumed constant part of the run-off into that lake, 0.004 foot of depth on the lake 
area per day, was never increased or decreased on any day by the assumed variable 
part of the run-off. On Lake Michigan-Huron, with much larger assumed R's, the 
variable part of the run-off was considerable. Note that in Table 37 the estimated 
variable part of the run-off shown in the columns headed +Rir x , -^-RiTi, +R,r,, 
. . . amounted to +0.009 foot on May 3, which increased the assumed constant 
part of the run-off, 0.006 foot to a total of 0.015 foot for that day. On May 9, on 
