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 sufficiently complete. The writer agrees with J. S. 
Moore 1 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 they 
would not have materially changed the new formula, inasmuch as 
Tutton used only four series, all of which were excluded by the 
writer because they were on other than wood-stave pipes. The 
close application of Tutton's formula to stave pipe, as shown by the 
consistent agreement in pipes all 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 deriving 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 all 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 all 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 he 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 c v , a^, b v , and c H , a^ b H , be, respectively, the V 
and H coordinates of the above centers of gravity. 
i Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 470. 
