44 BULLETIX 854, U. S. DEPARTMENT OF AGRICULTUEE. 
Trhen ^ equals 1 (wlien the tile is flo^^-ing full) and assuming the 
exponent of s to be 0.5 for all depths of flow, 
V=d1.2Q D'-''^' s'-^ (55) 
The similarlity of this formula to Pronj's formula in equation 7 
should be noted. 
A formula for the clay tile using only the data on the 5, 6, and 8 inch 
sizes (1-foot lengths) was derived, as well as a formula for the 10 and 
12 inch clay tile (2-foot lengths). These, however, were not deemed 
of great importance as indicating the effect of joints in the tile line, 
since an insufficient number of tile sizes were available for considera- 
tion. 
From a study of the data on the flow in tile running partly full, it 
will be seen that the velocity does not vary in accordance with the 
variation of the hydraulic radius. This fact suggested an attempt to 
derive a formula: that does not involve the hydraulic radius, but is of 
the type, 
y=(^y-' (56) 
That is, instead of the hydraulic radius, or the area divided b}^ the 
wetted perimeter, it was recognized that the area might have one 
exponent and the perimeter a different exponent. A careful study of 
this type of formula revealed the fact that it would be impracticable. 
Another type of formula which was considered was of the form 
(p^)V-^ (57) 
where A:, x, and C are unknown constants. This type was also con- 
sidered inadvisable. 
Still another formula considered was of the type 
where i^and /3 are constants and B is the breadth of the water surface, 
in the tile exposed to the ah. This t3'pe was investigated quite care- 
fully vdih the data relating to the concrete tile, but was not consid- 
ered applicable to the conditions. 
From a study o-f the velocit^^-depth of flow curves it will be seen 
that the greatest velocity m a pipe is approximately at 0.8 depth. 
Theoretically it would be at 0.81 depth. Below this the velocity 
decreases rapidly with the depth of flow. Observations on the flow in 
