A NEW METHOD OF ESTIMATING STREAM-FLOW 
213 
(1) The discharge observations were arranged in ascending order of magnitude 
in increments of one in the units used (or 0.001 cubic foot per second). In order 
to identify particular discharge magnitudes with the time of year on which they 
occurred, the listing of the discharges was made as a table of columns of dates, at 
the top of each column being placed a number, and under these numbers were 
written the dates when the corresponding discharges were observed. 
(2) The tabulations described in the preceding paragraph were summarized by 
writing in a vertical column the discharge values in ascending order of magnitude 
and, in an adjacent column, numbers indicating the total number of times that the 
corresponding discharge had been observed. 
(3) In a third column was written the differences between the S c discharge, 
108, and the discharge listed in the first column mentioned in (2), limiting the values 
used to those greater than S c . These differences are the v's of equation (94). 
(4) In a fourth column, the squares of the values of v of column 3 were written. 
(5) In a fifth column, the products of the values in columns 2 and 4 were 
written. The sums of these values became the 2(w 2 ) of equation (94). On Stream 
A, this sum was 52,328,754. 
(6) The total number of observations of stream-flow on Stream A greater than 
108 was 700 out of a total of 1,759 values of daily discharges during the time March 
9, 1911, to December 31, 1915, inclusive. It appeared that the discharges preceding 
March 9, 1911, may not have been as accurately determined as the later ones, hence 
they were rejected. The 700 is the N' of equation (94), which, substituted therein 
with the above value of 2(v 2 ) gives p. e. = 0.6745 
52328754 
700-1 
= ±184.6 
(7) This probable error, == 185, was arbitrarily taken as the class-interval to 
use in evaluating the constants of equation (96). In Table 60, the third column 
shows the 'total number of observations of stream-flow between the limits stated in 
the first column in increments of 185. The second column shows the deviation of 
each group in the third column from an assumed mean of 277.5. The values in the 
fourth to seventh columns inclusive are the products of the values in, respectively, 
columns 2 and 3, columns 2 and 4, columns 2 and 5 and columns 2 and 6. The sum 
of the products in columns 4 to 7, inclusive, are the first to fourth moments, respec- 
tively, of the data about the vertical through the assumed zero of 277.5. 
Table 60 — Moments of frequency curve of Stream A 
Limits of discharge (inclusive). 
Unit= 0.001 c.f.s. 
Deviation 
from 277.5 
Observed 
frequency 
Moments 
1st 
2d 
3d 
4th 
0— 185 
-1 

+ 1 
+ 2 
+ 3 
+ 4 
+ 5 
+ 6 
+ 7 
1,410 
2.34 
52 
39 
13 
3 
2 
1 
5 
-1,410 

+ 52 
+ 7S 
+ 39 
+ 12 
+ 10 
+ o 
+ 35 
+ 1,410 

+ 52 
+ 156 
+ 117 
+ 48 
+ 50 
+ 36 
+ 245 
-1,410 

+ 52 
+ 312 
+ 351 
+ 192 
+ 250 
+ 216 
+ 1,715 
+ 1,410 

+ 52 
+ 624 
+ 1,053 
+ 768 
+ 1,250 
+ 1,296 
+ 12,005 
185— 369 
370— 554 
555— 739 
740— 924 
925 — 1109 
1110—1294 
1295—1479 
1480—1664 
Totals 
1,759 
-1,178 
+ 2,114 
+ 1,678 
+ 18,458 
