A NEW METHOD OF ESTIMATING STREAM-FLOW 201 
The greatest percentage error occurred on December 15, 1914, when the com- 
puted discharge was 0.072 c.f.s., larger than the observed of 0.042 c.f.s., an error of 
71 per cent. 
A similar comparison of the extreme values on Stream B shows the following: 
The lowest daily discharge observed was 0.057 c.f.s. on September 12, 1915. 
The computed discharge on that day was 0.073 c.f.s., in error by 28 per cent or 
0.016 c.f.s. 
The lowest daily discharge computed was 0.064 c.f.s. on October 2, 1912. The 
observed discharge on that day was 0.100 c.f.s., in error by 36 per cent or 0.036 c.f.s. 
The lowest daily discharge computed was 0.007 c.f.s. greater (12 per cent) than the 
lowest daily discharge observed. 
The highest daily discharge observed was 1.966 c.f.s. on May 22, 1912. The 
computed discharge on that day was 0.565 c.f.s., in error by 71 per cent or 1.401 
c.f.s. 
The highest daily discharge computed was 0.974 c.f.s. on May 15, 1911. The 
observed discharge on that day was 0.563 c.f.s., making the computed discharge in 
error by 73 per cent or 0.411 c.f.s. The highest computed discharge was (1.966 — 
0.974 = ) 0.922 c.f.s. less than the highest observed discharge, or 50 per cent less. 
The greatest absolute error occurred on May 22, 1912, when the computed 
discharge was only 0.565 c.f.s., and the observed was 1.966 c.f.s. 
The greatest percentage error occurred on May 9, 1911, when the computed 
discharge was 0.520 c.f.s. larger than the observed of 0.366 c.f.s., an error of 142 
per cent. 
These comparisons of extreme values shows a considerably greater degree of 
accuracy on Stream B than on Stream A, as is to be expected. 
If the constants in these formulas were not true constants of nature, there 
would presumably tend to be a systematic change in sign of the residuals with the 
seasons. The residuals here referred to are the final ones, represented by the 
difference (total computed) — (observed) stream-flow. As a test of any seasonal 
changes in the difference "C — O" (computed) — (observed) flow, Tables 52 and 53 
have been prepared, representing the distribution of the residuals C — O. In these 
tables, for each year, there are two columns headed C— 0+ and C—O — . Under 
each is indicated by double and single vertical lines the time intervals during which 
the residuals were -f- and — , respectively. For instance, referring to Plate 10, 
the computed stream-flow was less than the observed from April 19 to August 3, 
1913. This is shown in Table 52 in the C — O— column for 1913 as a single vertical 
line. By glancing across the table, it is possible to detect any tendency for the 
residuals to be of the same sign at the same season of the year. An examination of 
the distribution of the residuals as shown in Table? 52 and 53 shows that there is 
little systematic change, except (a) that during the greater part of May in each 
year C — O is negative, the change from + to — always occurring on the down- 
ward slope of the computed curve of discharge for the spring flood; (6) that in 
August of each year there is a decided tendency of C — O to be +. In Table 53, 
comment (a) above is not so applicable. The change mentioned occurs less regu- 
larly and has shifted to a later time. 
Note that on Stream A, the cause of the systematic change (a) is the disagree- 
ment in time of the computed and observed spring-flood peaks and centers of 
gravity. On Stream B this was removed, partly by having more accurate values 
of C, F and M, and R' n , R' n , R' /»> • • • R ' n> and partly by estimating the last 
