218 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
From the above table it is seen that the maximum error in an individual value 
is 30 per cent, and it is estimated that the maximum error in the mean value ob- 
tained on any stream with two years of record of discharge will be about =•= 10 per 
cent. 
The S e estimated for any stream by this device becomes the R" of equation 
(59), page 148. A least-square adjustment based upon, say, 200 daily observations 
on the stream should serve to give the correction R of equation (60) to this R", 
with a probable error which should be nearer 5 per cent than 10 per cent of the true 
S c , R+R". The constant, S C) is rather difficult to determine for a stream from the 
least-square computations alone when one knows nothing of its probable magnitude. 
Incidentally, therefore, by estimating it in this manner, one can derive a quick, 
accurate correction to it to get the true value. 
The frequency-ratio curves on Plate 20 all follow the same general course. 
They show that the observed frequency of discharge of the streams as smoothed- 
off by Pearson's curves all bear in general a similar relation to the symmetrical 
probability curve. The ratio curves for Streams A and B tend to follow each other 
more closely than the other two, which is to be expected from the comparative 
amounts of data used in establishing them (see Table 63). The weighted-mean 
values of these ratios shown in the last column of Table 66 are the best values 
obtainable in this investigation, and are assumed to be constant for any stream in 
a moist climate. The weighted-mean values of the ratios are shown plotted in the 
upper left-hand corner of Plate 21. From the weighted-mean values, it appears 
that the minimum ratio is about 0.40, and it occurs at a discharge of about 2.0 
times the p.e. plus S c . The curve at a p.e. of 6 or greater rises very rapidly. At 
the two points where this ratio curve is unity are the places where the corresponding 
symmetrical probability curve would intersect the fitting frequency curve. These 
two intersections occur between and 0.5 p.e., and between 3.5 p.e. and 4.0 p.e. 
Table 66 — Weiglded mean frequency ratios 
a/r 
Frequency ratio 
Stream A 
Stream B 
Cumberland 
River 
Delaware 
River 
Weighted 
mean 

0.5 
1.0 
1.46 
0.66 
1.08 
0.68 
0.74 
0.44 
1.18 
0.58 
0.53 
1.5 
0.48 
0.38 
0.53 
0.34 
0.43 
2.0 
0.43 
0.36 
0.49 
0.32 
0.40 
2.5 
0.45 
0.40 
0.53 
0.34 
0.43 
3.0 
0.55 
0.50 
0.64 
0.42 
0.53 
3.5 
0.76 
0.74 
0.92 
0.57 
0.75 
4.0 
1.19 
1.22 
1.46 
0.91 
1.20 
4.5 
2.10 
2.30 
2.63 
1.66 
2.18 
5.0 
4.20 
5.00 
4.80 
3.40 
4.43 
5.5 
9.3 
11.0 
12.4 
7.4 
10.1 
6.0 
23.3 
23.0 
28.0 
18.5 
24.8 
6.5 
By means of these ratios, one can estimate the probability of occurrence of 
any flood within the limits of the ratios on any stream as soon as the S c of the stream 
and its p.e. are known. For example, referring to column 8, Table 61, according 
to the laws of probability, 2 accidental errors out of 10,000 will occur between 5.5 
