48 BULLETIN 852, U. S. DEPARTMENT OF AGRICULTURE. 
glazed interior pipes. Class 3 was chosen from which to derive the 
value of x and of K 3 , using the 20-inch Temescal pipe (No. 18), sup- 
ported by Farming's experiments (No. 19) for the small size and the 
Catskill aqueduct 174-inch pressure tunnels for the large size (Nos. 
39 and 40). This class was chosen because the range between com- 
parable surfaces was greater than for any of the other three classes, of 
which classes 1 and 2 extend from 6 inches up to about 36 inches, and 
class 4 is represented by experiments on pipes from 30 to 63 inches 
only. 
The experiments upon the 20-inch and the 174-inch pipes men- 
tioned above were accepted as basic, partially because they were 
conducted upon relatively long reaches of pipe where conditions for 
experimentation were favorable, but for the most part because of 
their relative positions on Plate VI, as regards the positions occupied 
by points representing pipes which are known to have very smooth 
surfaces and pipes that are known to be rougher than modern practice 
will countenance, as well as lines that can be classed as " modern con- 
crete pipe," neither exceedingly smooth nor " mortar-squeeze" rough. 
From the centers of gravity for the 20-inch and 174-inch pipes, 
projections at a slope of 2 intercept the axis of H (line for V= 1) at 
0.2006 and 0.0125 respectively, from which values of m for their 
respective diameters, Kis computed as 9.4 and x as — 1.28. Since x, 
the exponent of d, was accepted as —1.25 by Schoder and other 
authorities, and the writer did not desire to alter existing formulas 
unless the necessary change is radical, he also accepted — 1.25 for x 
and recomputed K. The pivot for changing the slope from —1.28 
to — 1.25 should be for an average-size pipe rather than for a 1-inch 
pipe. A 42-inch pipe was accepted as about the average size; then 
substituting in formula 13, 
m= ' 28 , or log m = log 9.4-1.28 log 42 
from which m = 0.07859 for a diameter of 42 inches. 
With this value of m and —1.25 for the value of x, substitution in 
formula 13 gives 
0.07859 = K 42 - 1 - 25 , or log 0.07859 + 1.25 log 42 = log IL 
or 
log K= 10.92443, from which K=SA. 
Making the final basic formula for pipes of class 3 read: 
tj 8 - 4 F2 riri 
from which 
7=0.345 H - 5 d°- 625 = 1.63 H - 5 Z>°- 625 = 115 i? - 625 S - 5 (17a) 
and since Q = A V, then 
# = 0.00188 E - 5 d 2 -™ = 1.28 H»* D 2 -™ (176) 
