54 BULLETIN 376^ IJ. S. DEPARTMENT OF AGEICULTUEE. 



used as derived on page 51. The reasoning which recommended 

 revising the usual method follows: 



In Plate VI the curves for the pipes of small diameters intersect 

 the V=l line. These intercepts give the vahies of m. 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;, thal^ i^, 

 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^ (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-i-17 = 0.419 D-^-^^ (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-i-^7 ¥*•« = 0.419 D-^i^ V^-« 



becoming 



XT _ 7.68 V^-«_ 0.419 V^-« f.^. 



^ griT ^07 — ^^^f 



which is shown, with the related formulas, on page 7. 



