60 BULLETIN 194, U. S. DEPARTMENT OF AGRICULTURE. 
are designated by open circles and numbered to correspond with the 
numbers in column 1, Table I. For the same tests the values of R 
as ordinates are also plotted as dots. As a general statement there 
is a distinct tendency for n to decrease as the velocity and hydraulic 
radius increase, although in some cases the opposite effect is noted. 
The slope of the decrease in n is rather uniform, but the writer did 
not feel that the evidence was sufficient to attempt to deduce a 
formula to cover it. 
A chart showing this change for values of n usually assigned to 
earth channels has previously been published. 1 
CONCLUSIONS. 
A careful study of the data on the previous pages and of the ex- 
periments carried out by others appears to warrant the following 
general conclusions: 
(1) That Kutter's formula is applicable to the design of any open 
channel. 
(2) That the recommendations of the earlier writers concerning 
the values of n to be chosen were in the main correct. Any weak- 
ness was due to the fact that there was not sufficient distinction made 
between the various categories and that materials of construction are 
now used which were not covered by the tests from which early de- 
ductions were made. The influence of curves was not as a rule in- 
cluded. Concrete lining covered but one value of n, whereas in prac- 
tice there are many shades of roughness, all applicable under the 
general head of concrete. 
(3) That the factor n must include all the influences which tend 
to retard velocity. The principal of these influences are undoubtedly 
(a) rubbing friction between the water and the containing channels, 
and (b) vegetable growth extending into the main body of the water. 
The lack of carrying capacity in many channels is probably due to 
the fact that the first influence was the only one considered. Of 
secondary importance, but nevertheless deserving of careful consid- 
eration in about the order named, are the following : (c) Angles and 
sharp curves in the alignment, (d) Influences which tend to disturb 
parallel filaments of current. The concrete lining in a rough rock 
cut may be quite smooth to the feel of the hand and yet be so undu- 
lating as to cause heavy cross currents which retard velocity. All 
projections and irregularities in the bank of a canal disturb the fila- 
ments of current in addition to having a large area exposed to rub- 
bing friction, (e) Sand and gravel cause heavy loss in velocity when 
allowed to enter and accumulate in shifting patches on a lined canal 
bed. Fine sand drifts downstream in deep, irregular pockets and 
1 C. T. Johnson and R. D. Goodrich. A Formula and Diagram for Determining the Velocity of Flow 
in Ditches and Canals. Engin. Rec, 64 (1911), No. 19, p. 542. 
