52 BULLETIN 376, IT. S. DEPARTMENT OF AGRICULTURE. 
As the exponent did not appear to vary in accordance with any- 
particular law, but depended upon each individual pipe, the writer 
followed the authorities name above and derived one general value 
for this exponent. The method employed was as follows: 
Obviously one observation on a particular pipe gave no data of 
value in determining the slope of a line. Two observations at about 
the same velocity contributed little more, but two observations at 
widely separated velocities gave enough information to indicate at 
least a tendency. Ten observations over a very short range of 
velocities did not give results as dependable as the same number over 
a greater range. Likewise ten observations, eight of which were 
close together and the other two well apart, did not contribute as 
much as the same number of observations evenly distributed through- 
out the range of velocities. With these general arguments and Plate 
VI as a basis, three men outlined a system for weighting the various 
exponents in the individual pipe formulas. 
Four factors entered into this process : First, the number of obser- 
vations; second, the distribution of the observations as shown by 
the distance between the centers of gravity of the upper and lower 
zones of observations; third, the extreme range of the observations 
on the chart; fourth, the actual range of the velocities. Usually 
the weight factor for the number of observations equaled the total 
number of observations, but some of the series showed an excessive 
evidence in restricted zones with fewer data in other zones. As an 
example of this, see No. 41. One observation within each half- 
second of velocity range received full weight. Each additional 
observation within the same half-second of range received an addi- 
tional weight of half a unit. Thus the 1 1 observations in this series 
received a total rating of 8 for the number of observations. (See 
column 10, Table 3.) 
The study of the data was made on 10-inch base logarithmic paper. 
Each inch of distance between centers of gravity of the upper and 
lower zones received a weight of 1 in the second factor. Thus, No. 
41 was rated 1.6 in this factor. (See column 11, Table 3.) 
Each inch of distance between the extreme observations also 
received a weight of 1 in the third factor. Thus, No. 41 was rated 
2.8 in this factor. (See column 12, Table 3.) 
Each one-half foot per second of velocity between the extreme 
observations also received a weight of 1 in the fourth factor. Thus 
No. 41 was rated 3 in this factor as the range of velocities extended 
from 3.5 to 4.8 feet per second, a difference of approximately 1.5 feet 
or the equivalent of 3 X 0.5 feet per second. The total weight for this 
pipe was the product of these four factors, the equivalent of 
8 X 1.6 X 2.8 X 3.5 = 125. (See column 14, Table 3.) 
