THE FLOW OF WATER IN DRAIN TILE. 35 



Substituting in formula 14, 



s = eD xyz ( 17) 



This expressed in logarithmic terms is 



log s = log e+x log D +z log V (18) 



FORMULAE 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 1 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, 0, 

 shown by a solid circle (PL X, fig. 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 line 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. 



