THE FLOW OF WATER IN DRAIN TILE. 35 
Substituting in formula 14, 
s = eD^V^ (17) 
This expressed in logarithmic terms is 
log s = log 6+a; log Z>+s log F (18) 
FORMULA FOR TILE FLOWING FULL. 
In deriving the various formulae, both analytical and graphical 
methods were used in order to insure accuracy. Figure 1 of Plate X 
shows the results obtained by the analytical method for the concrete 
tile. This diagram was obtained by plotting the velocities of all the 
selected experiments in Table 4 ^ against their respective slopes. The 
centers of gravity of the various points for each size of tile were 
plotted, after being calculated as outlined below. Straight lines 
were drawn through these centers of gravity for each size. Thus a 
series of approximately parallel lines was obtained. It should be 
noted that in using the analytical method, equal weight is given to 
the least velocity and the greatest velocity. The slopes and intercepts 
of each of the lines on this diagram were determined analytically. 
The following description gives the methods of derivation. Taking 
the experiments in which the tile were approximately full, shown in 
Table 4,^ the center of gravity of all the points belonging to any one 
size of tile was determined as follows: The antilogarithm of the 
mean value of the logarithms of the various velocities gave the 
velocity coordinate of the center of gravity; the slope coordinate of 
the center of gravity was found in a similar manner. This point, C, 
shown by a solid circle (PL X, ^g. 1), divides the plotted points into 
two groups. The center of gravity of the two groups separated by 
the principal center of gravity must also be found. These points, 
A and B, are shown by open circles. Having these two points, the 
equation of the Hne for that particular size of tile and depth of flow 
can be readily determined, as shown by the following sample calcula- 
tion for 4-inch concrete tile: 
Let C= center of gravity of the whole group. 
A = center of gravity of the part of the group above C. 
B = center of gravity of the part of the group below C. 
1 The serial numbers of these selected experiments are indicated in Tables 3 and 4. 
