92 BULLETIN 316, U. S. DEPARTMENT OE AGRICULTURE. 
guide as the present state of knowledge makes possible. The writer thinks all 
who have been concerned in experimental work of this character must recognize 
that a close approach to exact agreement among results is not to be expected. The 
author's analysis of the conditions affecting the reliability of the experiments is very 
thorough and his work seems to merit acceptance equally with the best previous 
results. Nothing occurs to the writer by way of criticism or discussion worthy of 
publication. 
Author's closure. — The apparent lack of conformity in results of hydraulic 
experiments has discouraged many observers. It would appear that carefully con- 
ducted experiments, made with the best of apparatus, should give results of extreme 
consistency. It is more than likely that results that should be consistent are so and 
that variations are due to influences that can not be seen or guarded against. The 
best that may be done is to anticipate all known abnormal conditions and either elimi- 
nate them or make corrections for them. 
Discussions of some experiments mentioned appreciated field difficulties. There 
is a vast difference between testing small pipes, weirs, or other devices in a hydraulic 
laboratory, where all of the factors are assuredly in the control of the observer, and 
testing large commercial structures in the field under varying weather conditions with 
unavoidable fluctuation in discharge of water and other difficulties that may or may 
not come to the knowledge of the experimenter during the tests. Seldom it is that a 
field layout approaches ideal conditions for experimentation. Except in rare cases 
tests of commercial plants must be foregone if laboratory conditions are to be met. 
"When apparatus is set up for test in a laboratory, minute measurements of diameters, 
water volumes, and other factors may be made. Both interior and exterior may be 
examined with microscopic care. In field tests of pipes, on the other hand, it is not 
often that water may be withdrawn for sufficient time to enable the experimenter to 
fully acquaint himself with conditions that are ordinarily hidden. 
Probably the most accurate series of tests of record are those conducted by Saph and 
Schoder on brass pipes. The largest of these was slightly more than 2 inches in diam- 
eter. With all the accuracy the experimenters could bring to bear upon these tests in 
a hydraulic laboratory, the results were such that they qualified their derived formula 
with a factor of ±7 per cent. 1 
THien the above qualification is necessary for a formula based on laboratory tests on 
pipes having uniform structural characteristics which have never been subjected to 
deposits, growths, or tuberculations. what is to be expected of a formula for use in the 
design of wood-stave pipes based on pipes taken as they come in the field ? Can such a 
formula show more than the new formula shows in Table 2 and on Plate VII? Except 
in isolated cases this agrees within ±15 per cent with more than 250 observations on 
52 pipes from 1 to 162 inches in diameter. Furthermore, more than half of these pipes 
are siphons on irrigation projects; that is, pipes inserted between open sections of canal 
from which all manner of trash, silt, and rock ravelings may enter the pipe and retard 
the flow. These are unavoidable conditions in the operation of such pipes, and the 
author would not confine his tests to pipes under more nearly ideal conditions, even 
if such might be chosen. These conditions must be anticipated by the designer and 
some suitable factor of safety introduced as is suggested on page 66. 
The above is not offered by way of apology for the new formula but to make clear 
the fact that the actual discharges from pipes designed on the basis of the new formula 
are not to be expected to agree with the formula values exactly but only to a reasonable 
degree. 
The author agrees with Mr. Williams and Mr. Xoble that experimental errors, due 
to erroneous assumptions of pipe diameter, may creep into the results. These errors 
i Trans. Amer. Soc. Civ. Engin., vol. 51 (1903), p. 306. 
