A NEW METHOD OF ESTIMATING STREAM-FLOW 221 
has gradually changed in the sense that more has remained accumulated in the 
parts of the area remote from the stream and that there is less storage near the 
stream. 
Assume, on the other hand, that on a specific day there is neither rain nor net 
melting and consequently a decrease in storage, and that thereafter for 256 days 
there is no change in storage in any day, the rainfall or net melting on each day 
being just sufficient to equal the evaporation plus stream-flow. Then, according 
to the theory developed by this investigation, the reverse of what has just been 
described will take place. The influence of the specific day in decreasing the flow 
of later days will be indicated in turn by negative values of rji'i, r 2 R\, r 3 R' z , . . . 
r, M'l o. At the end of the 256-day period the total storage will be unchanged. But 
its horizontal distribution will be changed in the sense that there will be less storage 
in areas remote from the stream and more near the stream. 
In the actual case which occurs in nature, there is either an increase or a 
decrease in storage on each day. According to the theory of this investigation, 
each day initiates a train of events like one or the other of the two just described. 
The actual stream-flow of any day is the aggregate of 257 such trains. Such an 
aggregate is represented by the formula given for the normal stream-flow. 
In an ideally perfect theory, of course, infinity should be substituted for 257 
and the series of such terms as r x R'i, r 2 R\, r,R' t , . . . should be infinite. To date 
it has not been found feasible to trace the influences back more than 257 days, that 
is, to determine any term more remote than rio-R'io in the formula. 
The theory embodied in the flood-flow formula is (a) that a flood-flow is initiated 
only when the ground near the surface is glutted with water; (&), that the best 
available index of glutting is the size of the stream-flow on the preceding day com- 
bined with the intensity of the rainfall on the current day; and (c), that when the 
n for a given day is above the value, G, which produces a glut for that day, a flood- 
flow is produced for 33 days thereafter, following such a law as is embodied in the 
formula. The constants of the flood-formula R' fx , R' n , R' H, • • • R' H are to be 
derived from the observations. It is expected that expressed as percentages the 
first three will ordinarily be greater than the last three on any stream to which this 
method is at present limited; that is, the summit of the flood-flow is expected to 
occur very soon after the maximum rain or net melting which produced it, and 
thereafter the flood-flow will gradually diminish to zero at the end of a period which 
for Streams A and B is not less than 33 days long. 
It is believed that flood-flow is produced mainly by certain portions of the 
stored water traveling an unusual proportion of the trip toward the stream over the 
surface of the ground, or very near the surface, and so producing an unusual horizon- 
tal distribution of the underground storage. It is not believed that in general a 
large proportion of the flood-flow travels the whole trip to the stream over the 
surface. 
The theory embodied in the freezing-melting theory is (a) that in general there 
is a constant tendency for melting to occur on the lower side of the mass of snow, 
ice and frozen earth, which tendency is offset partially or wholly by a tendency to 
freeze, which is proportional to the negative temperature reckoned from the critical 
point, T" ; (b) that the melting at the surface is proportional to the positive tem- 
perature reckoned from the critical temperature T"; and (c) that the critical 
temperature, T", is below 32° F. by somewhat less than the daily range of tempera- 
