12 BULLETIN 193^ U. S. DEPAETMENT OF AGEICULTUEE. 
may overflow and the pumps be flooded, for short periods, but it , . 
seems economicafly impracticable to provide against such unusual i j 
conditions. 
RUN-OFF FORMULA. 
Many attempts have been made to devise a mathematical expres- 
sion involving various of the factors that modify the maximum 
run-off rate, for use in estimating run-off when there are not actual 
gagings that will serve as a fairly reliable guide. A formula has been 
suggested by S. W. Frescoln for computing the run-off depth to be 
expected from any simple drainage area. It is as follows: 
^ BL 
in which 
Z) = maximum rate of run-off, in inches per 24 hours, to be 
expected from the rainfall P. 
6'=a coefficient depending solely upon the physical character 
of the soil, and determined by experiment. 
J/= the ratio of total run-off to total rainfall, for the precipita- 
tion P, varying with evaporation, deep percolation, lateral 
seepage from the drainage channels, and duration of flood. 
P = the depth of rainfall in inches in 24 hours (4 inches for 
Jefferson County). 
P=the average slope of the ground surface of the drainage 
area, in feet per mile. 
X = the mean length of the drainage area in miles. 
P = one-half the mean width of the drainage area in miles. 
For drainage areas that contain storage reservoirs, a special cal- 
culation must be made to eliminate the effect of the reservoirs. 
Where the main watercourse is formed by the junction of two or more 
large tributaries, the formula is to be applied to each tributary 
separately, and the proper value of the run-off depth for the entire 
area will be the weighted mean of the values for the parts. 
APPLICATION OF THE FORMULA. 
The values of L, B, and F are determined from the drainage sur- 
vey, P from rainfall data as already explained, M and C by com- 
parison with other drainage basins where gagings and other flood 
data have been secured. 
The value of ■^[F is determined for each simple drainage basin by 
first dividing the area into units wherever there is a marked change 
in the surface relief, as where a flat area joins a rolling or hilly section, 
each unit wholly on one side of the main stream. The mean -yfF is 
found for the course which the water will take from each corner of 
the unit to the outlet of the whole basin and the average of these 
