52 BULLETIlSr 376, U. 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 hne. 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 outhned a system for weighting the various 

 exponents in the individual pipe formulas. 



Four factors entered into this process : First, the numiber 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 fuU 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-haK 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 



8X1.6X2.8X3.5 = 125. (See column 14, Table 3.) 



