38 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTUflE. 
The line representing equation 22 is shown in figure 1 of Plate X. 
The mean hydraulic radii in the above computations were obtained 
by averaging the hydraulic radii for the selected tests in Table 4 for 
each size of tile, and not by using -j, because these radii are for 
tests varying from 95 per cent full to full. The mean hydraulic radii 
have been plotted as abscissae with their respective revised intercept 
values as ordinates. These points are designated in the figure by 
stars. The centers of gravity as computed above havo also been 
plotted, and a line drawn through them. Substituting in equation 22 
transposing, and using the center of gravity just computed. 
Log <s=logm'-(- 1.3128) log i? (23) 
= 6.874896+1.3128 X9.20479 
and 6 = 0.00006775 
Thus 
m' = 0.00006775 i?-i-3i28 (24) 
where 0.00006775 is the intercept on the line B = l, and - 1.3128 is the 
inclination of the line to the horizontal axis. The logarithmic 
diagram showing the development of the line for equation 24 is shown 
in figure 1 of Plate X. A similar line for clay tile is shown in figure 1 
_of Plate XL 
Substituting equation 24 and the mean value of s (p. 40) in the 
general formula 17, this general equation is now obtained for concrete 
tile: 
S = 0.00006775 i^-l-^lSS 1^1.96433 
0.00006775 V'^''^^ ,^«>, 
From this, solving for F, we get 
V= 132.5 i?«'««« s«-5«^ (26) 
which is the formula derived analytically, using the mean hydraulic 
radii for the selected experiments for each size of concrete tile in 
Table 4. 
In a like manner, the formula as derived analytically for clay tile 
was found to be 
V = 134.7 R'-^'^ s'-^'^ (27) 
The data used in deriving equation 27 for clay tile are shown on figure 
1 of Plate XL This diagram has been prepared similarly to the 
diagram in figure 1 of Plate X, except that the values used are from 
the selected tests in Table 3, for clay tile. 
Formulae 26 and 27 were derived by the analytical method, using 
only experiments with the tile flowing from 95 per cent full to full, 
