142 A NEW METHOD OF ESTIMATING STREAM-FLOW 
G t )+MO+Mt- , nM\+ 
+B^.r(n.-(? l )+2 l (C)+2 s (e-nMl+i2^.r(n.-G.)+2,(C)+2.(«-7 , "')Jlf"|-l- 
+i2' /7 |"(n 7 -(? 7 )+2 7 (C)+2 7 (i -T")M\-D'=-D (42) 
In equation (42), the sum of the terms£ c to#', [n, o+2, ,(C) -2, .(2* - O^+Sw 
(J — T")M], inclusive, express the normal part of the stream-flow. This is equation 
(33) rewritten with r h r 2 ,r,, . . . no defined as in (41). The terms R' f i[(ni — Gi) + 
C+(t-T")M] to E' /7 [(n 7 -G 7 )+2 7 (C)+2 7 (f-r / )M], inclusive, express the 
"Flood-flow" part of the stream-flow, or equation (37) rewritten with r i} r 2 , . . . 
r 7 defined as in equation (41), except that the terms like — (T" — t)F, —H i (T" — t)F, 
. . . — 2 7 (T" — t)F have been omitted because a flood-flow can not be initiated on 
a day when t < T" . 
D in that part of the stream flow which is not accounted for in terms of S e -\- 
R\n l +R\n,+ . . . +i2' 10 n, and R',i(n 1 -G l )+R' Jt (n,-G t ) + . . . +R' f1 
(n 7 — G-,) ; in other words D is that part of the stream-flow which is to be accounted 
for as fully as possible by C, F, M and T". 
For convenience in equation (42) let 
S.+R f in 1 +R' t n i +R'»n,+ . . . +i2'„n„ = D „ (43) 
and 
R* ,i(«,-&)+12' ttfa-G^+R' „(«,-<?,)+ . . . +R' n {ri 1 -G 1 )=D t (44) 
the latter equation being confined to days affected by flood-flows, when there is 
plenty of snow and ice available for melting, then 
D n +D,-D'=-D (45) 
in which D is that part of the stream-flow to be accounted for in terms of C, F, M 
and T". 
Now, in equations (42), (43), (44) and (45), the following quantities are 
assumed to be known before C, F and M can be determined from (42). These 
quantities (I) to (IX) are assumed to be known as estimated, derived from previous 
least-square computations, or directly observed: 
(I) S c , R\, R\, R\, . . . R' n , which are assumed to be known, as assumed or 
derived from previous least-square computations confined to normal stream-flows 
in the summer months; 
(II) R'f h R' f2 , R'/t, . . . R' fn , which are assumed to be known, as assumed 
or derived from previous least-square computations confined to flood-flows in 
summer months; 
(III) The n's, which can be computed from observed or estimated quantities 
of rainfall, evaporation and run-off as defined in equations (40) and (34) ; 
(IV) D' ' , which is the directly observed stream-flow; 
(V) Values of G (the T\ required to glut the ground before a surface flow is 
initiated) for various D"s, which are determined from the computations which 
yield (I) and (II); 
