46 BULLETIN 852, U. S. DEPARTMENT OF AGRICULTURE. 
In Plate VI the loss of head per thousand feet of pipe, H, for each 
observation on concrete pipes, is platted on logarithmic paper as an 
ordinate against the corresponding value of the mean velocity, V, as 
an abscissa. For a given series of observations the resulting curve 
represents equation 12 in its logarithmatic form 
log 5" = log m + z log V (16) 
which is now recognized as the equation of a straight line where m 
is the intercept on the axis of H (which is the line V= 1) and z is the 
tangent of the angle between the curve and the axis of V (indicated 
by a on PI. VI). 
A study of this plate, in connection with the descriptions of the 
various pipes, shows that pipes of the same structural characteristics 
follow a rather definite order of position on the plot. If all of the 
curves were of the same inclination to the axis V, then this order of 
position would be definitely and fully disclosed by a diagram in which 
the values of m are platted on logarithmic paper as ordinates and the 
diameters of the pipes, in inches, are platted as abscissas. The 
experiments upon some of the pipes, of necessity, covered such a 
short range of velocities that the curves indicate a slope quite at 
variance with that which would have probably resulted for more 
complete series. For this reason the writer has not projected the 
curves to an intersection with the axis of H, in order to determine the 
relative positions of the values of m. Obviously some system of 
weighting should be assigned to the various series and, in the study 
of experiments upon wood-stave pipe, an arbitrary weighting method 
was employed; but because there was some criticism of this pro- 
cedure the writer hesitates to repeat it. 
If all the pipes were made in the same manner, had the same 
interior surfaces, and were subject to the same hydraulic conditions, 
a law derived by the method of least squares should be the best and 
most accurate. This method of handling experimental data, however, 
ascribes all variation from a given law to errors, according to the 
probability of errors, whereas most of the variation from an average 
law of data on commercially made concrete pipes is due to inherent 
differences in the pipes. 
For any given series of experiments upon the same pipe the method 
of least squares is applicable, in its simplest form; that is, by the 
center-of-gravity method. 1 This method was used in computing 
the individual formulas given in column 10, Table 4. The curve is 
represented graphically in Plate VI, where the center of gravity of 
all the points in any one series is shown as two circles around a 
center which is typical of the observation points for that particular 
series. That is, if the observation points are given as open circles, 
i Described in Bui. 376, U. S. Dept. Agr., p. 50, and in Amer. Civil Engineers Pocketbook, 3d ed.,Ne\v 
York, 1916, p. 847. 
