A NEW METHOD OF ESTIMATING STREAM-FLOW 139 
which result entirely from percolation and not from waters traveling over the sur- 
face of the ground to the stream, the estimate of the run-off for the current day is 
usually correct on the first trial, and is best estimated in terms of the computed D' 
for the preceding day. During a rising stream it may be necessary to add to the 
D' of the preceding day (converted to the same units as n) to get the estimated 
run-off of the current day. During a falling stream, it may be necessary to sub- 
tract. In either case the change one way or the other is gradual for the class of 
flows to which equation (33) applies, hence the estimate, with a little practice, is 
easily made correct the first time. 
FORM OF EQUATION FOR FLOOD-FLOW 
During periods of heavy rain or rapid melting of snow and ice, the ground 
becomes saturated, the "water-table" rises above the surface of the ground, and 
there is a rapid travel of some of the water toward the stream by surface flow. This 
surface travel of the water is much more rapid than travel through the ground, and 
gives rise to quick and large flows which follow a different law of stream flow at 
such times than if the normal underground lines of flow were followed. Two lines 
of evidence lead to this conclusion; one being the internal evidence of the least- 
square solutions themselves and the other certain external evidence. This evi- 
dence will be presented at an appropriate place in connection with discussing the 
"Form of Observation Equation for Determining Flood-Flow." 
Whenever the rainfall (or its equivalent in melted snow and ice) exceeds, in a 
given drainage area in any day, a quantity which will be called G (in depth over 
watershed), on the basis of this investigation to date, the flood-flow of the stream, 
or that part of the stream-flow which travels over the surface of the ground to the 
stream, may be effectively expressed by the following formula: 
r / ,fi / /I +r / ,fl' /1 +r / J2 / /l +r / «fl' /< +r / J2' /l +r / J2 , ,.+r / 7i2 , ,7 = Flood-flow (37) 
In equation (37), r / i = (r 1 — G), r f2 = (r 1 — G) for the preceding day, r /t = 
(r» — G) for the day before the preceding day, and so on, the quantities r /i} 77,, 
r>», . . . r n bearing the same relation to each other as has been indicated for 
fi, r t , r,, . . . r,„. All negative values of r n are ignored. 
G for any day bears a fixed relation, determined from the computations, to 
the discharge, D' } on the day before. 
R'/i, R'/t, R'/,, . . . R'/7 are physical constants which express the effects of 
only that part of the change in storage in the drainage area which occurs above the 
ground surface on the current day, preceding day, day before the preceding day 
. . . next preceding sixteen days, respectively, on the surface run-off or flood- 
flow the current day. That is, the R'/s bear the same relations to the change 
in storage above the ground surface as the R"s bear to the total change in storage, 
both above and below ground. 
During periods of flood-flow, the total flow of the stream is given by equations 
(33) and (37). It should be evident therefore that during periods of flood-flow, to 
compute the total stream-flow for the current day, one must, besides estimating 
r x for the current day as described on pages 138 and 139, also estimate r /u This 
makes the procedure of computing the total stream-flow from equations (33) and 
(37) a slower process in times of flood than when the stream is fed by percolation 
only. 
