A NEW METHOD OF ESTIMATING STREAM-FLOW 197 
ACCURACY OF THE COMPUTED FLOOD-FLOW 
The flood-flow constants of Streams A and B are shown summarized in the 
right-hand side of Table 51. The probable errors for these constants were not 
computed. During times of flood, the changes in stream-flow are large and rapid, 
as contrasted with the small changes in rate of flow which normally take place 
during flow fed by percolation only. For this reason it is certain that the accuracy 
of the derived flood-flow constants is of a much higher order than that of the normal 
flow constants. For instance, if one assume that on Watershed B a rain heavy 
enough to supersaturate the ground occurs, followed by no rain large enough to 
supersaturate the ground for a period of 32 days thereafter, 0.37 per cent of the 
gain in storage produced by this rain will be delivered to Stream B on each of the 
17th to 32d days, inclusive, thereafter. This is represented by the constant R' /7 = 
+3.11, expressed as a percentage. The error in this 0.37 per cent is probably much 
less than =±=5 per cent, the error in the corresponding normal-flow constant, R'-, 
V .059 / 
As another test of the accuracy of the computed flood-flow, consider the prob- 
able error of a single observation. On Stream B, the probable error of a single 
observation, computed rigorously from the normal equations and from the residuals 
of the 166 observation equations from which the flood-flow constants in Table 51 were 
derived, was ±20.0. This includes the probable error of a single observation of the 
normal stream-flow, =*= 8.4. This means that on any day picked at random, on 
which there is a flood-flow, the chances are equal for and against the proposition 
that the total computed flow (normal -(-flood) will be in error by less than 20.0 or 
0.020 c.f.s. 
The probable errors used as a basis for the foregoing discussion of the accuracy 
of the computed normal stream-flow and of the computed flood-flow are obviously 
too small to represent the truth. The approximate theory based upon the approxi- 
mate assumptions would necessarily introduce systematic errors into the computa- 
tions, the effects of which, upon the probable errors, would be difficult to estimate. 
It will be shown later in the discussion of rainfall, net melting, evaporation and 
run-off on Stream B, that the indicated accuracy of determination of the melting 
constant, M, is probably fictitious to some extent. 
TESTS OF OVERALL ACCURACY OF COMPUTED STREAM-FLOW 
If one insert the constants S c , R\, R't, R'%, . . . R'io, R'/i, R' n, R' fs , . . . 
R' }7 , C, F, M, T" and — - as derived separately for Streams A and B into the general 
formulas, equations (33), (34), (36) and (37), the resulting specific formulas are 
those for which it is claimed that the discharges of Streams A and B may be com- 
puted for any day provided the necessary meteorological observations are available. 
As a test of the theory, and of the accuracy of the derived constants, the discharges 
on Streams A and B have been computed from the formulas for each day from 
March 1, 1911, to December 31, 1915, and the computed stream-flow for each day 
has been compared with the observed stream-flow. 
The comparison of computed stream-flow with observed stream-flow will be 
given in such form as to help the reader to reach his own conclusions on certain 
pertinent questions. Are the formulas with the constants in them mere interpola- 
