50 BULLETIN 376, U. S. DEPARTMENT OF AGEICULTUEE. 



adding no significant information, would have required a far larger 

 diagram than that presented here. With the exception of these 

 tests, therefore, data were plotted for all known observations where 

 records were sufB.ciently complete. The writer agrees with J. S. 

 Moore ^ that — 



In preparing a tentative formula for general use all complete data, which can be 

 accepted as criteria for the loss of head in wood pipe, should be recognized in arriving 

 at a conclusion. 



However, in deriving the new formula, tests made on round wood- 

 stave pipe only were considered, in view of the proposed use of such 

 a formula. The comparatively close agreement between results 

 by use of the new formula and by the Tutton formula, as shown by 

 Tables 2 and 3, indicates that had the excluded tests been used threy 

 would not have materially changed the new formula, inasmucJh as 

 Tutton used only four series, all of which were excluded hy the 

 writer because they were on other than wood-stave pipes. The 

 close appUcation of Tutton's formula to stave pipe, as shown by the 

 consistent agreement in pipes aU the way from 4 inches to 144 inches 

 in diameter, is a remarkable coincidence, since his base data included 

 no stave pipes whatever and but one round pipe. 



In deri'ving the new formula the following methods were used: 

 After the observations had been plotted the diagram was used 

 merely as a sketch, all slopes and intercepts being determined analytic- 

 ally. Where the test on any one reach of pipe included several 

 observations the procedure observed was that used in the following 

 example : 



Take the writer's series 3 (Nos. 272-281, inclusive) on the 144-inch 

 Altmar pipe. The center of gravity of aU the points was first deter- 

 mined. The antilogarithm of the mean value of the logarithms of 

 the respective velocities gave the velocity ordinate of the center of 

 gravity. The slope ordinate of the center of gravity was found 

 similarly. This point, c, shown by a dot within two circles (PI. VI) , 

 divides aU the plotted observations into two parts. The center of 

 gravity of each of these parts was found by using only the observa- 

 tions within the zone of the part. These points, a and b, are shown 

 by dots within single circles. Thus three points are found, all of 

 which lie on the straight line representing the equation for that 

 particular reach of pipe. 



Let c = center of gravity of whole group ; a = center of gravity of the 

 part of the group above c ; b = center of gravity of the part of the group 

 below c; and let Cy, ay, by, and Cg, a^, bg, be, respectively, the V 

 and H coordinates of the above centers of gravity.' 



1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 470. 



