168 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
Month 
Observation equation 
Month 
Observation equation 
1911 
July 
Aug 
Dec 
1912 
Jan 
+ 1R+ 2i?„>+36 = » 
+ 1R+ 9Ri +50 = v 
+ liJ + 21ft, +44 = i! 
+ 1R+ 10flio+ 24 =« 
+ 1R- 3flio+ 7 = v 
+ 1R- l«io+15 = » 
+ 1R+ lftio+17 = c 
+ 1R+ ORiq- 2 = v 
+ 1R+ 9i?i - 2 = » 
+ 1R+ 8Ri + l = v 
+ 1R+ 7R l0 + 8 = v 
+ 1R+ 5Rio+ 7 = v 
1913 
Jan 
+ 1R- 4H 10 - 7 = v 
+ 1R- 6B10+ = v 
+ 1R+ lflio- 2 = i) 
+ 1R+ 3R i0 + l = c 
+ IR+ IR10+ 1 = » 
+ 1R+ OR10+ 13 = » 
+ 1R~ 5Bio+ 11 = d 
+ 19/?+58ifi +222 = 
Feb 
Oct 
Dec 
Sums 
Feb 
Mar 
Aug 
Sept 
Oct 
Dec 
The normal equations for Solution P formed from the observation equations 
shown above, are as follows: 
+ 19#+ 58fli„+ 222 = 
+58#+ 944R,„+ 1732 = 
(75) 
The solution of these equations give the following values for the two unknowns : 
R=-7M fiio=-1.365 
Applying these values (corrections) to the S c and R\ a , respectively, of Solution 
N, equation (73), there is obtained the corrected values of those unknowns as 
follows: S c = +116-8= +108; B' l0 = +2.17-1.36= +0.81 
Writing in these values in equation (73) in place of the values there shown, 
and combining R\ a and R\ b into the single constant, R' t , there is obtained for the 
final equation of normal-flow for Stream A the following: 
+ 108 + 0.28r 1 +0.21r 2 +0.14r 3 +0.109r 4 +0.84r 6 +0.69r 6 +0.62r 7 +0.58r 8 +0.44r 9 + 
0.81r 10 = D' (76) 
which is of the form of equation (33). 
Converting the new value of R'i into a percentage, there is obtained (+0.81 X 
0.0107 = ) 0.0087 per cent as that part of a change in storage on a specific day which 
is delivered to the stream on each of the 129th to 256th days thereafter, in place 
of the 0.023 per cent previously obtained. Multiplying this by 128, there is 
obtained 1.11 per cent as the total part of the change in storage on a specific day 
which reaches Stream A by underground travel during the subsequent 129 th to 
256th days thereafter, in place of the 2.94 per cent previously obtained. Using 
the new value of R'k, expressed as a percentage, 0.0087, in connection with the 
smoothed-off values of the other R"s of equation (73), shown in column 9 of Table 
44, there is obtained 9.0 per cent, in place of the preceding values of 13.6 and 10.9 
per cent, as the total part of the change in storage on a specific day on Stream A 
which is delivered to the stream by underground travel during a period of 257 days 
thereafter (and including the specific day) if during the 256-day period following 
the current day the storage is held constant. Note that it is the above value of 
R' 10) expressed as a percentage which is shown in the curve on Plate 8. Note also 
that the .Rio of equation (74) is a second correction to the assumed value of R' 10 , or 
R" l0 , of equation (66). Thus, the final corrected value of R' 10 = +0.58 + 1.586 
-1.36= +0.81. 
