174 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
of the flood-flow not accounted for by r fl R" f i-\-r fi R" H-\-r f Jl" /,+ . . . , which is 
to be accounted for by r /1 R / i-\-r /1 Rft+r/sRft+ .... These values of F are 
shown in the observation equations on page 172. 
The following is an example of the computation of r n , from which r /2 , r lx , . . . 
r f i follow according to the definitions previously given. 
Table 47 — Example of computation of r/i, r/ 2 , r/ S , . . 
Solution K, Stream B, October 1911 
Date 
ft 
G 
r/i 
1911 
Oct. 4 
+ 62 
47 
+ 15 
5 
+243 
46 
+ 197 
6 
- 13 
20 
7 
- 10 
20 
8 
- 10 
20 
9 
- 15 
etc. 
20 
In the second column of Table 47 are shown values of r x computed as already 
explained in connection with Stream A, pages 151 and 154. The unit is 0.01 inch. 
Values of G in the third column were selected from the tabulated values in 
Table 46 in connection with the observed stream-flow. For example, on October 
3, 1911 (Plate 13), the observed stream-flow is shown to be 93, which, by interpola- 
tion in Table 46, gives a value of G of 47 for October 4. On October 4, the 
observed stream-flow was 97, which gives a value of G of 46 for October 5. On 
October 5, the observed stream-flow was 398, which gives a value of G of 20 for 
October 6, and so on. 
In the fourth column are shown values of r fl , which are obtained by subtracting 
values of G from values of r x in the two preceding columns. 
Preceding October 4, 1911, and throughout the remainder of October, after 
the 5th, no other values of n were great enough to produce flood-flows (see Plate 
13) hence the whole of the computation of r tx , r /2 , r /l} . . . r /7 for October 1911 
results from the two values -f-15 and +197 shown above. As an illustration (refer 
to Example of Computation of —F and Observation Equation for Flood-Flow) take 
the observation equation for October 9, 1911. For that date there are only two 
r/s as shown, viz, r /4 =2(r/i for October 5 and 6) = +197. r /s =2(r/, for October 
1 to 4 inclusive) -T- 10 = 15 -T- 10 = 2 to the nearest even unit. The other r/s for 
October 9 are blank, because the r/s involved in their determination are all blank, 
The computation of all the other r/s shown can be verified according to the 
definitions previously given. 
EXAMPLE OF NORMAL EQUATIONS FOR FLOOD-FLOW. STREAM B 
In each least-square solution for determining the flood-flow equation, a set of 
normal equations was first formed in the usual way from the observation equations 
for each day. Then these sets of normal equations, one set for each group of days 
involved in a flood and its after-effects, were combined by addition to form the final 
set of normal equations for the whole solution. 
The normal equations for October 4 to November 6, 1911, in Solution K, 
Stream B, formed from the observation equations for that group of days partly 
shown on page 172, are as follows: 
