THE FLOW OF WATER IX WOOD-STAVE PIPE. 49 
to have been used to any great extent, probably for the reason that it 
was based on tests covering only a few pipes, namely, a 4-inch pipe 
tested by Noble and Harris, Adams's 14-inch and 18-inch pipes, 
Noble's 44 and 54-inch pipes, and the Ogden tests of 1899 on the 
72-inch pipe (Nos. 20, 23, 41, 44, and 48, Tables 2 and 3, and PL VII). 
In 1911 E. A. Moritz proposed the fourth set of formulas 1 (see 
p. 6) with the following qualification: "This formula is not recom- 
mended for adoption until more data are available and some of the 
uncertain points have been cleared up." 
A fifth set of formulas is now offered by the writer, who has fully 
appreciated the inadvis ability of extending the number of formulas 
already existing except as must be required by continued investigation. 
His own experiments, especially those on large pipes, when studied in 
connection with all previous data, would seem to supply convincing 
proof that a new formula is needed. 
With the exception of formula 15 all of the formulas referred to 
are of the exponential type; that is, they are based on the fact that 
for any particular series of observations, if losses of head are plotted 
logarithmically as one set of ordinates and velocities as the other, 
the resulting points will lie more or less along a straight fine. Such 
a straight line on logarithmic paper represents an equation of the 
form 
H = mV z (17) 
which, expressed for logarithmic study, may be stated 
log H = log m + z log V (18) 
where m is the intercept on the axis of H, for V = 1 foot per second 
and z measures the inclination of the line, being the tangent of the 
angle which it makes with the axis of V. 
For a series of pipes of the same general characteristics but of 
varying diameters the values of m follow the general equation 
m = Kd x (19) 
Substituting in formula (17) 
H = Kd x V z (20) 
This expressed logarithmically becomes 
logH = logK + xlog d + zlogV (21) 
Smith's tests (No. 1) were made on a pipe too small for any irri- 
gation usage and the graphic representation of the results, while 
i Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 442. 
42463°— Bull. 376—16 4 
