THE FLOW OF WATEE IN WOOD-STAVE PIPE. 53 
No pipe was permitted a greater weight than 1,000 in determining 
the exponent of V. If the product of the four factors exceeded 
1,000 no additional weight over the 1,000 was assigned. 
The writer is aware of the arbitrary character of this method of 
determining the exponent, but it was obvious that some system of 
rating must be assigned and the one used appears to give about 
the right weight to the various pipes when Plate VI is studied. The 
proof of the relative accuracy of this method is shown in Tables 2 
and 3 where the mean of all observations entering into the derivation 
of the general value of the exponent agrees with the formula to 
within -0.33 per cent. (See foot of column 19, Table 2). The 
mean value for all the pipes entering into the derivation of the 
exponent agrees with the formula to within +0.66 per cent. (See 
foot of column 18, Table 3.) 
Letting W 2 , W 4 , W 5 , etc., be the weights for Nos. 2, 4, 5, etc., in 
column 14, Table 3, and E 2 , E 4 , E 5 , etc., be the exponents of V in 
formulas for Nos. 2, 4, 5, etc. (column 17, Table 3), then 
W 2 E 2 + W 4 E 4 + W 5 E 5 + W 52 E 52 _ z _ 
W 2 + W 4 + W 5 + w 52 
In deriving the values of the coefficient K and the exponent x, 
the writer has not pursued the usual practice. This is to plot and 
study logarithmically the various values of m (found in a similar 
manner to m on p. 51) and corresponding values of d as ordinates 
and abscissas, respectively. 
The exponents of V in column 17, Table 3, vary within rather wide 
limits. The new general formula accepts a weighted mean value 
of this exponent, 1.803. Instead of using the values for m as taken 
from column 17, Table 3, the writer drew lines at the constant inclina- 
tion 1.803 from the center of gravity of all the points in one series 
to the line where V equals 1 foot per second (the line for pipe No. 
51 being shown in dot-dash in PI. VI). This revised value of m for 
each series shown in Plate VI is found by the equation 
log m' = log H - 1 .803 log V (22) 
(substituting 1.803 for z and transposing equation 18). 
Again, taking No. 51 as an example: 
log m' = 9.8689 -(1.803 X 0.8267) 
log m' = 8.3784 
m' = 0.0239 
By the method usually employed the value of m (0.0202) shown 
in the formula for No. 51, column 17, Table 3, would have been 
