54 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE. 
used as derived on page 51. The reasoning which recommended 
revising the nsual method follows: 
In Plate VI the curves for the pipes of small diameters intersect 
the V=l line. These intercepts give the values of in. Likewise, 
the lines drawn from the centers of gravity for these curves at the 
constant slope 1.803 give intercepts m' not far, as a rule, from m. 
Thus not very much difference appears for the smaller pipes; but 
out in the zones of curves for the larger pipes the average velocities 
are so much higher, and consequently the centers of gravity are so 
far from V= 1, that the difference between m. and m' is very marked. 
The revised method places all curves on the same footing; that^ is, 
the intercepts for the large pipes will have no more influence on 
the general formula than the intercepts for the small pipes. Using 
this method a line at the constant inclination 1.803 may be drawn 
through the point representing but one observation and a value 
of m ; found that is of weight in determining the general formula, 
whereas this same point contributes nothing toward the determina- 
tion of the exponent 1.803. 
The values of m' for the various series are shown in column 16, 
Table 3. In order to derive the term Kd s (formula 19), figure 4 
was platted logarithmically with values of m' as ordinates and of 
d as abscissas. 
The center of gravity of all the points is shown by the dot within 
two circles while the centers of gravity of the zones above and below 
this point are shown as dots within single circles. These three 
dots lie in the same straight line represented by the equation 
m' = 7.68 d" 1 - 17 = 0.419 D~ 117 (23) 
where 7.68 is the intercept on the line d= 1 and — 1.17 is the inclina- 
tion of the curve to the horizontal axis. 
Substituting in the general formula (20, p. 49), the general equation 
is now evolved for wood-stave pipes, either jointed or of continuous- 
stave construction, based on the weighted average condition of all 
round stave pipe upon which accepted experiments have been made. 
This formula is 
H = 7.68 d" 117 Y 1 - 8 ^ 0.419 D~ 117 V 1 - 8 
becoming 
tt_ 7.68 V 1 - 8 0.419 V 1 - 8 no v 
11 JOT 0Tl7 ^ 1Z ' 
which is shown, with the related formulas, on page 7. 
