220 A NEW METHOD OF ESTIMATING STREAM-FLOW 
evaporation or as stream-flow he certainly would understand the laws of stream- 
flow. The water in the drainage area during the period named is believed to be 
underground as a rule. Only a very small proportion of the water which appears 
as stream-flow travels over the surface of the ground on all, or much, of the dis- 
tance from the point where it falls to the stream. As a rule its trip to the stream, 
if it escapes evaporation, is a slow underground trip occupying many days. The 
ground in the drainage area, with its constant topographic relief and its constant 
underground natural drainage system, is the controlling part of the mechanism 
which gathers in the rain and transmits it to the points where it is evaporated, or 
to the stream. The ground is sensibly constant in such of its characteristics as 
affect stream-flow, except as changes are produced by man. 
In any case in which man does not, by dams or artificial drainage systems, or 
other interference with nature, produce changes in the stream-flow, all of the 
influences upon stream-flow which do not change with lapse of time are expressed 
by the 23 constants of the formulas for each of Streams A and B — 
S C) the R"b, the R'/s, C, F, M, G, T" and §-. 
lijv, 
Such influences are the topography, the geology, the surface conditions, etc. These 
derived constants are the autograph of the particular stream. They express its 
character. The constants will be different for each stream because the topography, 
geology, underground drainage system, etc., are different for each stream. 
The meteorological conditions change rapidly and irregularly from day to day. 
These changes are observed and are put into the formulas as the r's, the t's, etc. 
The formulas as a whole state that the flow of a given stream will always be the 
same under identical past meteorological conditions, and they express the variations 
of the flow in terms of the variations in meteorological conditions. 
Review the definition of S c given on page 211. Assume here, again, for con- 
venience, that on a specific day there is rain or net melting sufficient to produce a 
gain in storage and that thereafter for 256 days there is no change of storage on any 
day, the rainfall or net melting being on each day just sufficient to equal the evapo- 
ration plus stream-flow. Then, according to the theory developed by this investi- 
gation, the influence of the specific day in increasing the flow during later days 
would be that indicated by the terms TiR'i, r 2 R'2, r 3 R' 3 , . . . r 10 R'io; the r, (gain in 
storage) of the specific day becoming the r 2 of the following day, the r 3 of the next 
day following, and so on. In the assumed case rain or net melting would be added 
each day, uniformly distributed over the whole drainage area, and water would be 
subtracted each day by evaporation equivalent to a layer uniformly distributed 
over the area. In sharp contrast the water subtracted by stream-flow each day 
from the drainage area comes at first from the stream itself and areas very close to 
its banks; later from slightly more remote areas and only after many days from 
the most remote areas. Under these circumstances the added flow (added to S c ) 
produced by the increase of storage of the specific day will tend to be relatively 
large while it is being drawn from the near areas, will decrease as the areas drawn 
upon become more remote and will tend to become relatively very small after the 
lapse of many days. The R"s and R'/s expressed as percentages, therefore, will 
tend to be relatively large soon after the specific day and decrease gradually toward 
a minimum. Under the conditions described the total storage in the drainage area 
has remained a constant. But its horizontal distribution over the drainage area 
