A NEW METHOD OF ESTIMATING STREAM-FLOW 
191 
group of dates used in the illustrations, 
following tabulation. 
Thev are written out as shown in the 
Example of observation equations for determining C. F. M. and T', Solution A A ^ am A 
Daif- 
Observation equation 
Date 
Observation equation 
1913 
1913 
Mar. 14 
+8C-S3F+ 03/ — 10 = r, 
Apr. 1 
+ 11 < -'■' =H» 
15 
+7C-84F+ 03/- 9 = r s 
•> 
-11 C-75F+38Jf-210=«M 
16 
+8C-81F+ 03/- 4 = r, 
-11 C-7-F- 
17 
-7'/-7-F- 03/- 7 = r, 
4 
+ 9*C-77F-:«3/-H^ = »b 
18 
+7C— 78F4- 0J/- 9 = r s 
5 
- B*< -75F-273/-213 = r B 
19 
+SC-77F- 03/- S = r« 
6 
-\ T-74F— 413/-2>l=r»« 
20 
--< 7—79P+ OJf- 10 = r 7 
7 
+ 10*C-74F-423/-27> = r„ 
21 
+8C— 7ftF+ OJf- -> = r s 
8 
— 10*C-74F-433/-245 = rn 
o<> 
-Tr-7f,F- \M— 13 = r, 
9 
- »*C— 78F+33Jf— 179= - 
2.3 
— ~r--^F J - 03/- 13 = rn 
10 
+ 9*C— 17F+2Ml—U> = . 
24 
--C-^2F- OJf- ll=r u 
11 
-75J -23/-122 = r M 
25 
- : - ■ 
12 
+ 9*C-71F-2-33/-169 = n, 
26 
+8C-N3F- 03/- S = n, 
27 
+7C— 88*"+ 03/- 10=. , 
15 
+ 14 C-6&F-7^3/-532 = m 
28 
+7C-SJF— OJf— 19 = n 5 
16 
+15*C-69F-i-993/-633 = r«j 
29 
+SC-S2F- 13/- 36 = n. 
30 
+7C— 79F+ 43/- 67 = n 7 
31 
+9C-7-F-213/-1-- : 'i = t- ; 
*These values differ slightly from those computed on p3ge 186 because of a numerical error discovered ia 
the computations after the completion of Solution .4.1. The computations on page 186 are correct. 
These equations are written out in the form of equation (46). The coefficients 
of C, F and M or x, y and z, respectively, and the absolute term. —D, are copied 
from the computations of those quantities on pages 179 to 190, inclusive. 
The 32 equations are part of the larger group of 137 equations used in Solution 
AA, Stream A, which served to fix the values of C, F. M and T" derived from obser- 
vations on that stream. 
The observation equations were normally written in groups of a month apiece, 
and the normal equations formed for each group in the usual way. These normal 
equations were then combined by addition into a final set of normal equations. 
FINAL NORMAL EQUATIONS. SOLUTION AA. STREAM A 
The final normal equations for Solution AA for 137 days, formed from 137 
observation equations like and including the above 32. are as follows: 
+ 9,119 C- 76.890 F+ 13,996 -V-105.22S = D 
-76.S90 C+705.001 F-69.75S Af+585,775=0} 
+ 13,996 f - 69.75S F-72.774 .V- 474.246 =0J 
This final set of normal equations for Solution A A 90) depends upon 137 
observation equations on the following dates: February 14 — April 19, 13 — May 1. 
3-6, 1912, and February 14-April 1. 4-12. 15-16. 1913. inclusive. 
The solution of the final normal equations for Solution AA, (90), gives the 
following values for the unknowns : 
C=+S.59 = 1.16 F= +0.647 = 0.117 M= -5.49 = 0.123 
The probable errors shown were computed rigorously from the normal equa- 
tions (90), and from the residuals, v. of the 137 observation equations of Solution 
AA. 
90 
