A NEW METHOD OF ESTIMATING STREAM-FLOW 
i«.i:; 
(91) 
C=+3.97 ±0.71 
F= +0.457 ±0.055 
Jlf=+5.19 ±0.07 
7" = 28° F 
These final values agree so closely with the values used in estimating the dates 
to use in computing D f , that little or no change in those dates would be caused by 
using these more exact values. Hence the only assumptions on which these values 
depend directly are Assumptions Nos. (9), (10), (11) and (12). 
The freezing-melting curve, based on these values, is shown plotted in the 
lower left-hand corner of Plate 22. 
The unknown T" can not be determined directly from the observations. It 
can be determined only by trial. The value at first was assumed at 30° F., with 
Table 50 — Best values of C, F and M 
Beat value of C 
Solution A A, Stream A 
Solution X, Stream B . 
Best value of F 
Solution A A, Stream A 
Solution X, Stream B . 
Best value of M 
Solution A A, Stream A 
Solution X, Stream B. 
Probable 
Assigned 
error 
weight 
±1.16 
0.0741 
±0.712 
0.197 
±0.117 
7.30 
±0.062 
26.04 
±0.123 
6.62 
±0.083 
14.51 
Value of- 
C+8.59* 
+ 3.97f 
F +0.647 
+ 0.403 
M+5.49 
+5.04 
Residual 
-3.36 
+ 1.26 
-0.190 
+ 0.054 
-0.30 
+0.15 
Sum of 
weights 
0.271 
33.3 
21.1 
Weighted 
+ 5.23 
+ 0.457 
+ 5.19 
Probable 
error of 
weighted 
mean 
±0.61 
=0.055 
= 0.07 
Rejected. 
f Adopted best value of C. 
which value the derived value of C was positive and real, hence in the next least- 
C 
square solution, the corrected value of T"=T" — — , which came out 29° F., was 
used. With this value of T", C still came out positive on both streams and, after 
a careful study of the residuals, proof was obtained that T" = 29° F. was too large. 
The final reduction to 28° F. was accordingly made. The evidence as to whether 
T" = 28° F. is still too large is weak and inconclusive. Note the rather poorly 
determined value of C above. The true value of T" may be 27° F. The true value 
would make C zero, or it would come out poorly determined — that is, with a large 
probable error, which would give it the character of an accidental error. 
The evidence external to the least-square solutions indicated that the true 
value of T" is about 28° F. This consisted of a study of the daily and hourly tem- 
peratures and the daily and hourly discharges for February to May 1912 and in 
the spring of 1913 on Stream B. 
Using the adopted values (91), equation (36), expressing the net melting on 
any day in terms of the mean air temperature, may be written 
Net melting on any i r - (28° - 1) 0.457 i 
day in 0.01 =+3.97+ or (92) 
inch of depth J l + (*-28°) 5.19 J 
