10 BULLETIN 376, TJ. S. DEPARTMENT OF AGRICULTURE. 
In 1899 the same experimenters made additional tests (No. 48) 
upon the same pipe with improved apparatus. 1 Their experiments 
were centered on a longer reach of pipe and a consistent set of values 
of n was obtained, ranging from 0.0130 to 0.0133. 
The trend of the discussion of the second Ogden tests shows that 
a general belief existed to the effect that the difference in the values of 
n, when compared with n for smaller pipes, was due to defects in the 
Kutter formula. 
A graphic presentation of the data then available was made on 
ordinary squared cross-section paper. In the discussion a method 
was offered for testing the correctness of experimental data by the 
use of this paper, "if the loss of head varies as the square of the 
velocity." 2 Although as long ago as 1808, Dr. Thomas Young 3 
suggested that the loss of head was in proportion to the 1.8 power 
of the velocity, rather than the second power, many still insisted 
that loss of head must vary as the square of the velocity. It is inter- 
esting to note that 1.8 is the exact exponent found by both Moritz 
and the writer, while Williams and Hazen use an exponent of 1.85 
in their general formula for flow in many kinds of pipes. 
In 1901 T. A. Noble 4 contributed greatly to the available knowledge 
by making tests on 44J-inch and 54-inch pipes (Nos. 41 and 44), 
thus bridging the gap between 30-inch and 72-inch pipes. For both 
these pipes the values of n ranged from 0.0120 to 0.0136, with the 
higher values in the smaller pipe, although the same water flowed 
through both pipes and they were constructed at the same time. 
Also, strange to say, the pipe with the lower value of n contained more 
curvature and growths of Spongilla which were not present in the 
smaller pipe. Noble says : 5 
The writer can offer no suggestion as to why the value of C should be less and n 
greater in the 44-inch than in the 54-inch pipe, when, to conform to the results of 
other experiments, it should be the reverse. 
In discussing the available data on this subject, 6 E. W. Schoder 
of Cornell University suggests the possibilities of an exponential 
formula derived from a study of the straight-line curves resulting 
when the losses of head are platted on logarithmic paper as ordinates 
and the velocities as abscissas. This was the method used later by 
Moritz in deriving his formula, and also by the writer as being the 
best known form by which to study the now extensive number of 
tests upon wood pipe. 
i Trans. Amer. Soc. Civ. Engin., 44 (1900), p. 34. 
2 Id., p. 73. 
3 Philosophical Trans., Royal Society of London (1808). 
* Trans. Amer. Soc. Civ. Engin., 49 (1902), p. 112. 
& Id., p. 143. 
e Id., p. 145. 
