170 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
and —D'. As a specific example, note that the value given in the R' t — column for 
June 17, namely, +10, is the product of the quantity +12 in the June 17 observa- 
tion equations, which is the coefficient of R\, times the final value of R' h namely, 
+0.84. The specific meaning of the +10 is that the total addition to storage on 
the watershed due to the rains of June 9, 10, 11 and 12 (Table 41) increased 
the stream-flow 0.010 c.f.s. above S c on June 17. The total water which passed 
through the ground to the stream on June 17 is given by the sum of the columns S e 
to rioR'io inclusive. This is found to be 0.110 c.f.s. The observed stream-flow on 
that date was 0.202 c.f.s., consequently the difference (0.110-0.202 = ) -0.092 c.f.s. 
is unaccounted for by equation (76). This 0.092 c.f.s., contains, in part the flood- 
flow for that date and all of the errors involved in the theory and the assumptions 
combined. Using the adopted criterion for flood-flow previously mentioned, viz, 
0.030 c.f.s. (page 167), the residuals of June 1913 show that on every day of that 
month part of the flow of the stream was delivered by surface travel or flood-flow. 
Referring again to Plate 10, the normal flow of the stream as computed from 
equation (76) is shown as a dash-dot-dash fine. S c or 108, the constant part of the 
flow, is shown as a light, solid, horizontal line, from which as a base line the jVs 
are plotted as a dotted line. The residuals, v, of the substitution in observation 
equations for June 1913 are shown on Plate 10, as the difference between the ob- 
served flow (heavy solid fine) and the computed normal flow (dash-dot-dash) line. 
The light dashed line (with triangles between the dashes) between the curve of 
observed flow and computed normal flow represents the total computed stream-flow 
as computed from equation (76), and the flood-flow formula of the form of equation 
(37), an illustration of the derivation of the constants of which will presently be 
given. 
EQUATION OF NORMAL FLOW OF STREAM B 
By methods already described on Stream A, the values in column 2 of Table 45 
of the constants in the normal-flow formula, equation (33), were derived from 
observations on Stream B in 1911 to 1913. 
Table 45 is comparable with Table 43, except that R\ is not divided into two 
parts, and that, since the unit used in computing r t was 1.0 inch of depth, the factor 
0.0119 for converting R'» to a percentage is the same as for R\ . In this table 1.19 
Table 45 — Conversion of normal-flow constants to "percentages, Stream E 
Constant 
Absolute value 
of constant 
Factor to con- 
vert col. 2 to 
percentage of 
change in storage 
which is deliv- 
ered in one day 
Per cent of 
change in storage 
which reaches 
stream on one day 
(col. 2Xcol. 3) 
No. of days or 
time interval 
involved in each 
constant 
Total per cent of 
change in storage 
current day 
which reaches 
stream in each 
time interval 
(col. 4Xcol. 5) 
S c 
+96.0 (±4) 
+ 0.060±0.021 
+ .071± .024 
+ .082± .031 
+ .079* .017 
+ .790± .088 
+ .715± .054 
+ .496± .029 
+ .269 — 
+ .403 — 
+ .210 — 
1.19 
1.19 
1.19 
1.19 
0.119 
.119 
.119 
.119 
.0119 
.0119 
0.071±0.025 
.084± .029 
.098* .037 
.094± .020 
.094=t .010 
.085± .006 
.059± .003 
.032 — 
.0048 — 
.0025 — 
1 
1 
1 
2 
4 
8 
16 
32 
64 
128 
0.071 
.084 
.098 
.188 
.376 
.680 
.944 
1.024 
.307 
.320 
R\ 
R' 2 
R' t 
R\ 
R'i 
R' t 
R' 7 
R\ 
R\ 
R' 10 
257 
4.092 
