230 A NEW METHOD OF ESTIMATING STREAM-FLOW 
tions (77) and (86), pages 171 and 177, respectively. The degree of accuracy with 
which it is possible to estimate the flow of these streams from their respective 
formulas in terms of the observed weather elements is stated in Table 54 to 59a, 
pages 205 to 207. 1 
The ratio of the frequency curve of discharge of a stream, for discharges greater 
than S c (the constant part of the flow), to the normal or Gaussian frequency curve, 
is believed to be the same for all streams in moist climates (pages 211 to 219). 
The larger part of the water which reaches a stream travels underground to the 
stream from the point where it falls as rain, or occurs as melted snow. Only a small 
part of it travels over the surface of the ground for all or much of the trip to the 
stream. On Stream A, for example, of any increase in storage in the ground which 
does not produce a flood-flow, only 9.0 per cent appears as extra stream-flow in 
257 days, if during that period the storage is held constant. On Stream B, only 
4.1 per cent appears as extra stream-flow in 257 days. Of that portion of an 
increase in storage which is above the limit produced by glutting, only 19.0 per cent 
appears as extra stream-flow in 33 days on Stream A, and 29.6 per cent on Stream 
B. These percentages, 19.0 per cent and 29.6 per cent, would each necessarily be 
much higher if much of the travel of the water were on the surface of the ground. 
The phrase "extra stream-flow" is meant to specify that part of the flow which is 
an excess above the constant part of the flow, S c (pages 163 to 168, 170 to 171, 
172 to 176, and 178). 
When there is an abundance of snow and ice available on a watershed for 
melting, there is a constant addition to the stored water in the ground equivalent 
to 0.0397 inch of depth per day when the mean air temperature on the watershed 
for the 24 hours is 28° F. For each day for each degree that the mean air tempera- 
ture for the day is less than 28° F. there is a subtraction of water from storage due to 
freezing at the rate of 0.00457 inch of depth per day. For each day for each degree 
that the mean air temperature for the day is greater than 28° F. there is an addition 
to the stored water in the ground due to melting at the rate of 0.0519 inch of depth 
per day. The rate of addition to storage by melting is therefore about 11 times 
greater than the rate of subtraction therefrom by freezing (pages 192 to 194). 
The average rate of travel of the crest of a flood wave throughout its trip down- 
stream is substantially a constant for all streams. It was found statistically to be 
44 miles per day, or 1.8 miles per hour, or 33 minutes to the mile. It is not fixed by 
accelerations, except in great expansions of the river — lakes — in which there is a 
negligible current (pages 224 and 225). 
This research may be applied to the following, among other, problems: (a) the 
problem of increasing the length of record of flow of a stream as a basis for greater 
accuracy in the design of engineering works for power, irrigation, navigation and 
sanitation, (6) the problem of forecasting the flow of a stream as a basis for increas- 
ing the economy of operation of hydro-electric power plants, (c) the problem of 
determining the effect of forest cover on the run-off from watersheds (pages 225 to 
229). 
1 The accuracy stated does not represent the best that can be done by the methods developed in this investi- 
gation. The figures in Tables 54 to 59a are taken from the computations representing various stages in the evolu- 
tion of the theory. If the theory as finally evolved, together with the best technique developed, were used, the 
accuracy stated could be increased. It appears that the annual aggregate stream-flow may be computed from 
the weather elements observed on its watershed with an error of less than 10 per cent on most of the years. 
