THE PLOW OF WATER 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 Wj, W4, W5, etc., be the weights for Nos. 2, 4, 5, etc., in 

 column 14, Table 3, and Ej, E^, E5, etc., be the exponents of V in 

 formulas for Nos. 2, 4, 5, etc. (column 17, Table 3), then 



W,E, + W,E, + W,E,+ W,,E33 __,_ . OQ^ 



W3+w,+w,+ w,, ^-^'^^-^ 



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 PL 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 



