98 BULLETIN 852, U. S. DEPARTMENT OF AGRICULTURE. 
The formula "T=130 R°- Q25 s °- 50 was suggested for new pipe (and 
otherwise with varying value of the coefficient) as being more con- 
sistent and quite as accurate as some other procedures that had 
preceded. 
Following this, ^ a simple hydraulic-slide rule was made to calculate 
pipe friction by it. This permitted a great increase in rapidity of 
estimate. The writer used these homemade rules for a year or two 
in his daily work, and made a number of them for his friends. He was 
well satisfied with the estimates that were reached by their use. Later 
the interest in hydraulic-slide rules increased, and there was a demand 
for more of them, and it was decided to have them made in quantity. 
Before doing this a careful reconsideration of the exponents was made 
by Prof. Gardiner S. Williams, which led to the adoption of those which 
have since come to be associated with the Williams and Hazen 
formula. 
This Williams and Hazen formula was intended to represent more 
accurately all round average waterworks conditions than the earlier 
one, which was identical with that one now proposed by the author, 
and the writer thinks that for such general use it is an improvement. 
It may be pointed out that a slight variation in the exponents does 
not make a very great difference in ordinary estimates. Precision in 
the values of the exponents is not to be expected and is not necessary. 
It is only desirable that the formula that is used should have exponents 
that do not differ too widely from the actual facts. 
With such a formula the important matter is a study of the coeffi- 
cients to find out whether these coefficients are affected by variations 
in the condition and smoothness of pipe surface, and by the character 
of the water that flows through the pipe. At the present time study 
of coefficients is much more useful than further study of minute 
differences in exponents. 
The writer is glad to see that the author is taking up his data along 
these lines. 
DISCUSSION BY MR. LIPPINCOTT. 
I have had a good deal to do with the construction of large concrete 
pipes, 10 to 12 feet in diameter, and the following observations may 
possibly be of interest: 
Concrete will expand and contract with wetting and drying in 
much the same way that it does between heat and cold, and in order 
to prevent shrinkage cracks coming from drying, the concrete pipe 
or conduit should be kept just as moist as possible during the period 
in vliich it is curing and until it has been actually put into service. 
In the case of large pipe particularly this can be accomplished by 
putting some water into the pipe and by closing the ends of the pipe 
after it is built so as to prevent the circulation of dry air through 
the pipe. I have known concrete pipe that has developed circular 
shrinkage cracks which leaked badly when water was first put in and 
to close up after the water had been running through them for seven 
or eight days, I believe because of the expansion of the concrete due 
to its becoming saturated. 
By taking pains in the manner suggested with the construction of 
the Los Angeles Aqueduct in the Mojave Desert, preventing the 
drying out of the concrete by circulation of air, mile after mile of 
this ditch could be built without any expansion joints and without 
any cracks developing. 
