12 BrXLETIX S->4. IT. S. DEP.IETMEXT OF AGEICrLTUEE. 
A new formula based on tests actually made on drain tile, derived . 
as hereinafter explained, is tentatively offered for tile flovring full. 
This formula is 
r= 138 i?M (13) 
It may seem that the exponential type of formula is inconvenient 
because logarithms must be used to calculate results from it. How- 
ever, it is comparatively simple in the case of such a formula to 
prepare a diagram or chart, composed of parallel, straight lines if on 
logarit hmi c scale, from which the rec|uii'ed velocity or the rec[uired 
discharge for any size of tile at any grade can be obtained at a glance, 
the acciu'acy of the reading depenchng entii'ely upon the scale of the 
diagi^am. Plate XIII is a diagram prepared by using the formula as 
derived from the actual tests made, but applied to commercial or 
nominal sizes of tile. 
It should be not^d that Ehiott's modifications of Poncelet's or 
Hawkesley's fonnula are the only ones which take into consideration 
the head caused by the water table in the soil, while the Chezy-Kutter 
formula is the only one in which the different retardation influences 
in clay and concrete drain tile may be considered. 
NECESS-\RY DATA FOR COMP.^RIXG VELOCITY FOR>IUL.^. 
In order to test the relative accuracy of the various formula? which 
have been recommended for use in determining the discharge of tile 
drains, the effect of each hydraidic element involved in the formulae 
must be determined by expeiim.ent. However, in the tests made at 
the experimental plant it was impossible to deteiToine the effect of 
the additional head caused by the water table in the soil. The ele- 
ments to be determined are as follows: (1) the m.ean velocity of the 
water in the tile drain; (2) the gi^ade or slope of the drain, or the 
water slope if it is different from that of the drain: (3) the internal 
size of the tile: (4 the actual depth of flow in the tile djrain. 
MEAN VELOCITY. 
The mean velocity of the water flowing in the drain can be deter- 
inined by various methods. However, only the following two m.ethod3 
were used: (1) by actually m.easuring the quantity of water entering 
or discharging from the tile drain per second, and then solving the 
equation V= — : (2 by timing a given volume of water through a 
previously measured distance. 
• HYDRAULIC GRADE OR SLOPE. 
The slope of the line of tile tested at the experimental plant was 
always kno^vn, since the tile were laid in an adjustable flimie which 
could be changed to the desired grade, the gi'ade always being checked 
bv a level. 
