138 A NEW METHOD OF ESTIMATING STREAM-FLOW 
observations themselves, as the evaporation from a free, open, water surface as 
6tated in equation (23), modified only by the constant — . 
E 9 
It is realized that Assumptions Nos. (6), (7) and (8) are approximations. 
Existing knowledge on these matters did not make possible a more exact expression 
at the outset. It was hoped that the deviation of the true laws of evaporation 
from land surfaces at all seasons of the year from those expressed in equation (34) 
could be detected from the observations themselves in this investigation, and that 
these deviations could be evaluated or expressed as modifications of equation (34) 
in definite terms. This hope was not realized, or rather, no proof was obtained 
that these approximations are far from the truth on Watersheds A and B. This 
evidence will be presented at an appropriate place later. 
{ -(T"-t)F } 
Net melting on any day = +C-f { or \ (36) 
i + (t-T")Ml 
Equation (36) is dependent on there being plenty of snow and ice on and in the 
ground of the watershed. In equation (36), t is the mean observed air temperature 
on the watershed for the day in degrees Fahrenheit; C, F and M are physical con- 
stants to be derived from the observations. T" is the mean air temperature for the 
watershed for the day in degrees F. at which there is assumed to be the same amount 
of melting as of freezing and therefore no change in storage in the drainage area 
due to melting and freezing. 
Equation (33) thus expresses the mean flow of a stream on any day as a func- 
tion of the changes in storage of water in the drainage area for a total period of 256 
days or 8.4 months preceding the current day. 
■pi 
The constants S C) R\, R\, R'%, . . . R\o, -=^, C, F, M and T" must ordinarily 
be derived from parallel observations of stream-flow and the weather elements. 
The last four constants, C, F, M and T" are believed to be the same for all water- 
sheds. They have been evaluated in this investigation from the observations on 
Streams A and B. The method of deriving the constants in equations (33) to (36) 
is discussed later. 
To compute the normal stream-flow for any day from the equation after its 
constants are evaluated, the observed weather elements of rainfall, temperature, 
vapor-pressure and wind velocity for the past period are substituted into the 
formula in accordance with the definitions of the quantities already given. The 
only quantity in Equation (33) which is not known on the current day, after the 
constants have all been derived, is r,, since the run-off for the current day is not 
known. It is the quantity wanted. The procedure is to estimate the run-off for 
the current day and compute an approximate r>. This enables one to compute D' 
for the current day. If this, when converted to the same units in which the r's are 
expressed, agrees with the estimated run-off for the current day, the computed D' 
for the current day is correct, and the computation may proceed to the computation 
of D' for the next day. If the D' computed for the current day differs from the 
run-off estimated for computing n, this estimated run-off must be changed until 
the computed D' for the current day agrees with the estimated run-off used in 
computing n. For flows to which Equation (33) applies, that is, stream-flows 
