136 A NEW METHOD OF ESTIMATING STREAM-FLOW 
From the above definitions of the r's, it is evident that it is only necessary to 
compute n for each day; that r», r,, . . . r 10 on any day may be written in directly 
from the values of n computed for preceding days; thus, 
r, for current day = ri for preceding day; 
r, for current day = r, for day before preceding day = r, for preceding day; 
r 4 f or current day = 2(n) for two days preceding day named in defining r, in terms 
of ri; = 2(r 3 ) on preceding and day before preceding days; 
r t for current day = 2(r,) for four days preceding days named in defining r t in terms of 
rij = 2(r«) on second and fourth preceding days; 
r, for current daj r = 2(n) for the eight days preceding days named in defining r« in 
terms of n; = 2(r t ) on fourth and eighth preceding days; 
r, for current day = 2(ri) for the 16 days preceding days named in defining r, in terms of 
r»; =2(r 6 ) on eighth and sixteenth preceding days; 
r 8 for current day = 2(a) for the 32 days preceding days named in defining r^ in terms 
of rjj =2(r 7 ) on sixteenth and thirty-second preceding days; 
r 8 for current day = 2(n) for the 64 days preceding days named in defining r 8 in terms 
of ri; = 2(r 8 ) on thirty-second and sixty-fourth preceding days; 
rio for current day = 2^) for the 128 days preceding days named in defining r, in 
terms of ri; = 2(r») on sixty-fourth and one hundred and twenty-eighth preceding 
days. 
It is thus apparent that by defining the r's in the manner stated, every r with 
subscript 4 or greater is the sum of two r's with subscript one less than the r wanted; 
and every r with subscript 3 or less (except n) can be copied from earlier r's. This 
device effects rapidity in computation. 
The above definitions will become clearer later in connection with the numeri- 
cal examples of the computations to be given. 
D' is the flow of the stream, usually, expressed in cubic feet per second, or 
some similar unit. 
R'i, R't, R's, . . . .R'io are physical constants which express the effects of the 
total change in storage in the drainage area both above and below ground surface on 
the current day, preceding day, day before the preceding day . . . next pre- 
ceding 128 days, respectively, on the flow of the stream the current day, or day to 
which the equation pertains. 
The evaporation from land is computed from the following formula: 
Evaporation from land = £,= [~0.319e-f 1.49e (^- 2 - 6 )](f L ) ( 34 ) 
In equation (34), E v = +0.3196+ 1.49e I jtt~ — 2.6 J is the evaporation from 
any free, open surface of water in units of 0.01 inch of depth per day anywhere in 
the United States where the observations of e and w are derived from standard 
Weather Bureau observations. This will be recognized as the evaporation formula 
derived from observations on the Great Lakes, or equation (23), page 82. In 
equation (34) e = (e a — e d ) in units of 0.01 inch of mercury, in which e a = saturation 
vapor-pressure corresponding to the mean air temperature over the watershed in 
0.01 inch of mercury; e d = saturation vapor-pressure corresponding to the tempera- 
ture of the dew-point, in units of 0.01 inch of mercury; w is the total travel of the 
