THE FLOW OF WATER IN DRAIN TILE. 11 
in which Vincent gives values for the variable coefficient, K, ranging 
from 0.75 for 2-inch tile to 0.875 for 6-inch tile. 
Friedrich^ states that Professor Gieseler's formula, 
7=36.22V^ (6) 
is the best in practice as well as the simplest. 
Formula 6 is said by Professor Luedecke to have, been deduced as 
early as 1852 by the agricultui^al engineer Stocken, at Schweidnitz, 
from Prony's formula, which is ' . 
F= 47.63 V^ (7) 
Beardmore's, sometimes called Leslie's, formula, 
V=im-ylRs (8) 
is similar to Chezy's, the coefficient (7 being taken as a constant, 100. 
The Williams-Hazen general formula for all kinds of pipes is 
F= O^R'-^H'-'^'Omi-'-'' (9) 
This formula is of special importance in this discussion, since careful 
comparison of it with the Chezy-Kutter formula has been made. 
C. G. Elliott, a ^videly known drainage authority, has modified the 
Poncelet or Hawkesley formula as follows:^ 
F-4S ipn+iE 
for use on systems where the soil is open; 
(10) 
7^48-./ -^ V^ + rj (11) 
V 1+54: D 
for use on large systems in close soil; 
(12) 
1+54: D 
for use on large systems in open soil. 
The last term in the numerator under the radical in formulae 10 
and 12 has been added to allow for the water pressure in the soil above 
the tile drain. This additional head, however, is constantly varying, 
being greatest when the earth is completely saturated. It is doubtful 
whether it should be used in computing the discharge of a drain, and 
if so, then only in open, porous soils. 
1 Friedrich, Kulturteehnischer Wasserbau, vol. 1, Berlin, 1912, p. 343. 
2 C. G. Elliott, Engineering for Land Drainage, New York, 2d ed., 1912, p. 93. 
