166 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
smoothing-out process is shown in columns 3 to 9 inclusive. Thus in column 3, 
line 4, the smoothed-off value of R' 4 , 0.096, is the mean of the three values 0.15, 
0.085 and 0.054 opposite it in column 2. The final smoothed-off curve appears in 
column 9, and column 10 shows the R"s of column 9 converted back to their regular 
form as in (71) by dividing by 1.07, 0.107 and 0.0107. The smoothed-off R"s at 
this point give 10.9 per cent as the total part of the change in storage the current 
day which is delivered to the stream in 257 days, assuming constant storage after 
the current day, as compared with 13.6 per cent for the unsmoothed values. 
The values in column 9 were taken as the best values of the R"s expressed as 
percentages which were obtainable from Solution M. These values (except R\<) 
are shown plotted on Plate 8. On this plate, the abscissas represent time in days 
and the ordinates the percentage of the change in storage, r i} on the current or 0th 
day, which reaches the stream on each day thereafter, assuming that no change in 
Table 44 — Smoothing-off R"s of Solution M, Strea?n A 
Constant 
R''s from 
Solution M 
First smooth- 
ing by means 
of 3 
Second 
smooth- 
ing 
Third 
smooth- 
ing 
Fourth 
smooth- 
ing 
Fifth 
smooth- 
ing 
Sixth 
smooth- 
ing 
Seventh 
smooth- 
ing 
Smoothed 
R"s 
R\ 
R's 
R\ 
R\ 
R'< 
R'i 
R'» 
R'n 
R\o 
p. ct. 
0.30 
.22 
.15 
.085 
.054 
.011 
.043 
.098 
.123 
.055 
.023 
.000 
0.03 
.22 
.15 
.117 
.090 
.074 
.066 
.062 
.054 
.041 
.023 
.000 
. .+0.28 
+ .21 
+ -14 
+ .109 
+ .84 
+ .69 
+ .62 
+ .58 
+ .50 
+ .38 
+ 2.17 
0.096 
.050 
.036 
.051 
.087 
.091 
.066 
.023 
.000 
0.099 
.061 
.046 
.058 
.076 
.081 
.060 
.023 
.000 
0.103 
.069 
.055 
.060 
.077 
.073 
.051 
.023 
.000 
0.107 
.076 
.061 
.062 
.068 
.065 
.049 
.023 
.000 
0.111 
.081 
.066 
.064 
.065 
.061 
.046 
.023 
.000 
0.114 
.086 
.070 
.065 
.063 
.057 
.043 
.023 
.000 
storage occurs after the current day. The horizontal scale is shown divided 
into time intervals corresponding to the various R"s, with the R"s indicated in 
the centers of their respective time intervals. The plotted points are shown con- 
nected by straight lines, although the actual facts presumably follow a smooth 
curve. Note that in plotting R' )a and R' ab , they were grouped together as R\ 
with the average value of 0.048 per cent. The small difference between R' ia and 
R' 9 6 apparently does not justify their separate determination. In other words, the 
run-off curve at this point is probably so horizontal that little gain in accuracy is 
obtained by separating R' 9 into two parts. 
NECESSARY ADDITIONAL ADJUSTMENTS TO NORMAL-FLOW EQUATION 
Obviously after smoothing off the constants, (71), in the manner described, it 
becomes necessary to make another least-square adjustment, using the same 
observations, for the purpose of compensating as much as possible for the changes 
made in that smoothing-off process. In this adjustment, which was designated 
as Solution N, all the errors introduced into (71) by the smoothing-off process were 
assumed to be thrown into the constant term, S c , and the adjusted value of S e was 
determined from the solution. The method of procedure was as follows: 
