ABSTRACT OF PROCEEDINGS. xliii. 
(37) 
in which « = about 0-77 andz = }. In order that m however, 
should be entirely general it is necessary to give it some such form as 
m=] 4 (37a) 
x 
“x+b(n-—1)° R* 
So that it may be always 2 when n=1 exactly. Experiment may 
therefore shew that it is always a function of the roughness. 
The general formula proposed is, for the mean velocity of the 
flow of water in a circular pipe under either régime, at any tem- 
perature, and with any radius, ‘slope,’ or material of pipe, 
i 1+4p wre 
U= () f°R I] (41) 
in which m depends upon the roughness of the channel, and can 
be set forth in categories, p and q are functions of the roughness 
expressed in m, and m is a function of the absolute dimensions of 
the pipe, sensibly, though perhaps not wholly independent of the 
roughness, but must be always takenas2whenn=1. The value 
of p is 0-256 (mn — 1); or more generally p =c(m—1)*. The 
defect of the Chezy, of the Darcy and Bazin, of the Ganguillet 
and Kutter, and of the Reynolds formulas, is that each systema- 
tically departs from what may be called the general trend or 
indication of the experiments upon which they are founded. 
The hydraulic radius is shewn, even in the case of the ellipse, 
not to be an absolutely satisfactory function in regard to eliminat- 
ing the influence of the form of a pipe or channel. What may 
be called the corrected hydraulic radius, is for the ellipse, 
Rg = R (1-3 6? $4 €* — ie Cee )eceoseees (47) 
in which 
e = (B-C)/(B+C). 
The general method of analysis of the flow in open channels 
was indicated, and the fact noticed that in this case m seems to 
increase with J, It is also noted that m increases with R which 
is clearly shewn in Series 23 of Bazin’s experiments. 
