106 A NEW METHOD OF ESTIMATING STREAM-FLOW 
And the total amount of r, which is delivered to the lake during the seventeen- 
day interval beginning with and following the current day is [100 .Ri + 100 Ri+ 
100 J2,+ (5.0)(2) Z2.+ (2.5)(4) i2,+ (1.25) (8) R t ] per cent, on the assumption that, 
following the change in storage on the current day, (rj), the sum of the evaporation 
from land and run-off from land are just equal to the rainfall on land on each day 
for a long time thereafter. 
Substituting the assumed values of R h R h R t , . . . R ,, (29) in this expression, 
it appears that 37 per cent of the change in storage in the ground on any day, r,, is 
assumed to reach the lake by the end of the sixteenth day thereafter, if, during the 
16 days following the r, there is no change in storage in the ground. 
In estimating the values of R\, Ri, R 3 , . . . R t to use in Solution Fiand 
previous solutions, they were first estimated as percentages, represented by the 
products of the various R's by the factors 100, 5.0, 2.5 and 1.25. Thus, the assumed 
R's, (29), expressed as percentages are 
fl, = + 1 fl 4 = +4.0 l 
R*= + 7 R b = +0.5 (30) 
R,= + 17 #,= +0.3 J 
An example of the meaning of this is that (5.0) (0.80) =4.0 per cent of r, is 
assumed to be delivered to the lake on each of the third and fourth following days, 
if no change in storage occurred after the current day or day on which the change 
in storage, r,, took place. 
The reason for estimating the values of the R's as percentages (30) is that it is 
easier to do it that way. The estimates so made are converted to the absolute 
values as in (29), by dividing by the appropriate factor 100, 5.0, 2.5, or 1.25. 
The estimates of the R's and of the E's (used in estimating the evaporation) 
depended upon (a) judgment, (b) internal evidence from previous least-square 
solutions, and (c) external sources of information in the engineering literature. 
In the very first least-square solution of a series, in which the observation equation 
of the form of (28) was used, the estimates of E lt E 2 , I C) R h R h . . . R t depends 
entirely upon judgment and information, such as could be obtained in the engineer- 
ing and scientific literature. As an example, for the first least-square solution on 
Lake Michigan-Huron in which it was attempted to evaluate simultaneously the 
evaporation and run-off by equation (28), a value for Ei was estimated as follows: 
The mean e for June 1910 for the Lake, computed as in the illustration on pages 25 
to 29, was 20, and for July 1910, 24. From the Monthly Weather Review, 
September 1888, the depth of evaporation, in inches, at signal service stations in 
thermometer shelters, computed from the means of the tri-daily determination of 
dew-point and wet-bulb observations, varied from 2.5 at Duluth to 4.9 at Rochester, 
with a mean of 4.1 inches for June 1888 for the 17 stations in the Upper and Lower 
Lake Regions. This averages 0.14 inch per day. 
Similarly from the same publication for July 1887, for the same 17 stations the 
computed evaporation varied from 3.4 at Marquette to 6.0 at Toledo, with a mean 
of 4.8 inches for the month, or 0.15 inch per day. Assuming all the evaporation to 
be accounted for upon an average by the term e £", and that June 1910 = June 1888 
0.14 0.15 
and July 1910 = July 1887, for June, ^ = -7^ = 0.0070 and for July ^,= -^ = 
0.0062. Or, as a mean, Ei = 0.0066 when the unit is the inch. But if the unit is 
