216 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
left indicates the frequency of discharge of Stream A. The lower scale of abscissas 
is the discharge of Stream A in 0.001 cubic foot per second. S c is shown at the 
discharge 108 of Stream A. With this S c as origin, the upper scale of abscissas is 
the discharge, D' , confined to values greater than S c , in terms of the p.e., which, 
for Stream A, is 185. This is also the scale of abscissas of the symmetrical proba- 
bility curve in terms of the increment a/r. 
Curve 1 on Plate 20 shows the observed histogram of Stream A, which is shown 
in column 4 of Table 61. The curve (equation (99)) starts at 0.078 c.f.s., and is 
shown above that point as a vertical line. 
Curve 3 on Plate 20 is the symmetrical probability curve plotted from the 
values in column 9, Table 61. 
Curve 4 (plate 20) is the ratio of the curve of stream-flow frequency calculated 
from equation (99) for discharges greater than S c , to the symmetrical probability 
curve. This curve is plotted from the values in column 10, Table 61. The vertical 
scale of curves 4, 5, 6 and 7 is shown at the right of Plate 20. 
Table 62 — Miscellaneous data on some streams 
Name of 
river 
A 
B 
Dix 
Cumberland . . 
Delaware 
Kankakee. . . . 
Length 
of 
period 
studied 
1911-15 
1911-15 
1918-20 
1918-20 
1918-20 
1913-15 
Limits of 
discharge in 
period studied 
Max. 
(c.f.s.) 
1.966 
1.645 
23,000 
43,500 
50,900 
2.60* 
Min. 
(c.f.s.) 
0.057 
0.041 
1.2 
41.0 
685.0 
0.02* 
Ratio 
max. 
min. 
discharge 
34 
40 
19,200 
1,060 
74 
130 
Drain- 
age 
area 
(sq. mi.) 
0.348 
0.313 
395 
2,040 
3,070 
4,600 
Annual 
rainfall 
(in.) 
20 
20 
45 
40 
50 
36 
Location of gaging 
station 
Wagon Wheel Gap, Colo. 
Wagon Wheel Gap 
Near Burgin, Ky 
Cumberland Falls, Ky. . 
Port Jervis, N. Y 
Kankakee, 111 
Discharge 
measured 
by— 
/U.S.W.B. 
lu.S.F.S. 
/U.S.W.B. 
\U.S.F.S. 
U.S.G.S. 
U.S.G.S. 
/U.S.G.S. 
\U.S.W.B. 
Power Co, 
* Unit is c.f.s. per square mile. 
In a manner similar to that just described in the numbered paragraphs 1 to 8, 
inclusive, for Stream A, the frequency ratio curves 5, 6 and 7, Plate 20, were worked 
out for Stream B, the Delaware River at Port Jervis, New York, and for the Cum- 
berland River at Cumberland Falls, Kentucky, respectively. The numerical values 
of these ratios are shown in Table 66, together with their weighted mean values, 
which were obtained by assigning the values the weights 2, 2, 1, 1, respectively in 
the order in which they appear in the table, to take account of the difference in the 
amount of data used, and to account for the fact that S c was determined on the first 
two streams from the least-square computations. Some characteristics of these 
streams are shown in Table 62. The histograms of the frequency distributions of 
the flows of these streams are not shown on Plate 20, neither are their fitting curves. 
The frequency distributions of these streams all required Pearson's type III 
curve for best representation. The values derived for the various constants in the 
general formula, equation (96), are shown in Table 63. Note that the criterion 
K is numerically greater than 4 in every case. Note also the rather large skewness, 
especially on Streams A and B. 
