A NEW METHOD OF ESTIMATING STREAM-FLOW 225 
The average rate of travel of 44 miles per day for the crest of a flood wave in a 
river was determined by a statistical study of the daily river stages as published by 
the Weather Bureau. In all, 15 rivers, located in all parts of the United States, 
were studied. The value 44 miles per day is based upon a study of 117 cases, each 
case being the observed rate of travel of the crest of the flood from one gaging 
station to the next one down stream on one river. A similar study of 10!) cases of 
the rate of travel of the end of the flood wave fixed it at 25 miles per day. In some 
cases the rate of travel appeared to be infinite; that is, the summit of the crest or 
end of the wave, as the case may be, appeared to arrive at two stations several 
miles apart on the same day. In other cases there appeared to be a negative rate 
of travel ; that is, the crest or end of the flood wave appeared to arrive at the lower 
of two gaging stations before it arrived at the next station upstream. Such cases 
as these two were rejected in arriving at the values 44 and 25 stated above. 
In this investigation the laws of stream-flow as stated were derived from ob- 
servations on two small watersheds. If this method is applied to a very large 
watershed, it is assumed that the n corresponding to each rain gage should be set 
forward according to the following rule: 
If the stream travel from the rain gage to the point of stream measurement is less than 
44 miles, no set forward; is between 44 and 88 miles, set forward one day; is between 88 and 
132 miles, set forward two days; and so on. 
Under this rule it is believed that the position of the maximum R' will remain 
unchanged as the total length of the stream travel increases. It is believed that 
the size of the maximum R' will be affected as follows: It w r ill tend decidedly to 
get smaller as the stream travel increases from zero to 44 miles, and for increases 
beyond 44 miles there will be a moderate tendency to get smaller. It will tend to 
be larger the more nearly each branch stream agrees in length of its stream travel 
with the total stream travel of the main stream above the mouth of the branch 
stream. 
As a first approximation it may be assumed that the rate of travel of a summit 
of thalweg travel is one mile per day. On this basis, one mile of length on an aver- 
age for each thalweg would tend to delay the maximum R' by about one day. 
The greater the variety of water travel by slope, thalweg and stream, the 
broader will be the summit of the R' or run-off curve. 
SOME POSSIBLE APPLICATIONS OF THIS RESEARCH 
During the course of this investigation several possible applications of the 
methods and constants developed became evident. It is proposed to set forth 
here briefly some of these possible applications. 
APPLICATION TO INCREASING LENGTH OF RECORD OF FLOW OF A STREAM 
Observations of stream-flow are used in connection with the design of future 
hydro-electric power plants, irrigation projects or water-supply projects in making 
estimates of the future mean flow, maximum flow and minimum flow. The more 
accurately it is possible to predict the flow of a stream, the more accurate is it 
possible to design the works with respect to economy and safety. The decision in 
the first place as to whether the waters of a stream can be economically utilized 
frequently hinges upon the amount of water available. 
