A NEW METHOD OF ESTIMATING STREAM-FLOW 143 
(VI) T", which is an assumption at first, later verified by least-square com- 
putations; 
(VII) Values of t, which are directly observed; 
(VIII) Values of (T" — t) and their S's, which can be computed from (VI) 
and (VII) ; and 
(IX) Values of (t — T"), and their S's, which can be computed from (VI) and 
(VII). 
If now all these known quantities, (I) to (IX), are substituted in the observa- 
tion equation, equation (42), and all similar quantities grouped and combined as 
far as possible, the observation equation for determining C, F and M may be written 
in the following form, one for each day : 
xC+yF+zM-D = v (46) 
In this equation, x, y and z are definite, known, numerical quantities, fixed by 
previous computations and by observed, assumed, or derived quantities as indi- 
cated in (I) to (IX) above. The specific definitions of x, y and z are as follows, as 
given in equations (47) to (55) inclusive: 
x = x n +x f (47) 
y=y»+y/ (48) 
z = z n +z, (49) 
In equations (47), (48) and (49), and referring to equation (42), 
(C)+i2 , .S.(C)+fl'„S„(C)]/C (50) 
and 
x / = [fl , /1 C+« / /iSi(C)-r-fl'/,S,(C)-r-/2 , ,42«(C)+fl'„S l (C)+i2',.S.(C)+/e'„2 7 
(C)]/C (51) 
the latter equation being confined to days affected by flood-flows, when there is 
plenty of snow and ice available for melting. 
y n =R\(t-T")+R'Mt-T")+R'Mt-T' , )+R'Mt-T'')+ . . . +R\£ l0 (t-T") 
confined to those cases in which t < T" (52) 
y f = 0, since for values of t < T" no flood-flow can be initiated (53) 
z n = R' l (t-T')+R'Mt-T")+R'Mt-T")+ . . . +# / 10 2 1 o(i-I w ), 
confined to those cases in which t > T" and there is plenty of snow and ice on and in the 
ground of the watershed available to be melted ; (54) 
z, = R' n {t-T")+R' n -LS-T")+R' Mt~T")+ . . . +R' 'Mt-T*), 
confined to days affected by flood-flows and on which there is an abundant supply of snow 
and ice on and in the ground of the watershed available to be melted (55) 
In equation (46) v is the residual, or the discrepancy between the computed 
net melting {xC-\-yF-\-zM), and D, that part of the discharge not accountable for 
in terms of equations (43) and (44). From a set of observation equations, values 
of C, F and M may be computed by the least-square method of computation. The 
substitution in observation equations furnishes a group of v's which serve to deter- 
mine the accuracy with which C, F and M have been derived from the set of 
equations. 
The complete meanings of all the terms involved in equations (42) to (55) will 
be made clear later in connection with numerical illustrations. 
