A NEW METHOD OF ESTIMATING STREAM-FLOW 141 
give the true temperature T' at which melting and thawing are just balanced is 
C 
T = — — . If the derived value of C is negative, the necessary correction to T" is 
F' 
On the basis just indicated, in which C is taken into account, the expression 
for r, as given in equation (38) must be modified to read as follows: 
r— (Observed rainfall) — (Estimated evaporation from land) — (Observed dis- 
r+C-(T*-t)F] 
charge) + or (39) 
{+C+(t-T")Mi 
In equation (39) if we designate by n h the following: 
nj = (Observed rainfall) — (Estimated evaporation from land) — (Observed discharge) . . (40) 
on the current day, then 
\= rii- 
(T"-t) F 
r,= |n,+C+ or 
i+(*-r') m 
(41) 
The values for r,, r„, r«, . . . r 10 of equation (33) may now be written in the 
forms corresponding to that shown for r x above, using the definitions given after 
equation (33). 
Each Ti, r», r s , . . . r I0 , for any date which reaches back in the computation to 
a day on which there was melting or freezing, will consist of a known numerical part 
made up of (observed rainfall), (estimated evaporation from land), and (observed 
discharge) — the n x of equation (40) — and an unknown literal part of the form 
f-(r-t)Fi 
+C+ I or \, the net melting of equation (36), in which the values of {T" — t) 
i + (t-T") M> 
or (t — T") are known from the observed temperatures and the assumed T". 
FORM OF OBSERVATION EQUATION TO DETERMINE C, F AND M 
On the basis of what has preceded, using equations (33), (37) and (41), we may 
now write the form of observation equation for determining C, F and M as follows : 
r [-(r-OFi] r r MT"-t)F } i r r 2,(r-0F,i 
S.+fl'i U.-I-C+ or +tf ',71,4-2,(0+ or +#', n,+2,(C)+ or + 
L i+(t-T")M\] L l+2,(*-r")MJJ L l+Mt-T")Ml] 
+R'I n<+Z t {C)-MT" -t)F+Mt-T")M~\+R\\ n t +Z s (C)-2 6 (r' -f)F+2 6 (<-r')M~| + 
+ fl^rn,+2,(C)-2 9 (r / -t)F+2,(i-r0Ml+fl',rn 7 +2 7 (C)-2 7 (r / -0F+2 7 (<-T' / )Ml + 
+fl^rn 8 +2 8 (C)-2 8 (r'-OF+2 8 a-roMl+ie%rn 9 +2 9 (co-2,(r / -OF+2,(<-r')M]4- 
+^orn 1 o4-2 1 o(C)-2 1 o(r'-0^+2 1 o(<-nMl+i2^ i r(n 1 -GO+C+(<-nM"| + 
