STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 355 
when n is very nearly 2. (2) The variation of velocity with respect 
to the radius of pipes also needs investigation: this evidently should 
be done with at least three series, having widely different degrees 
of roughness, so as to ascertain the influence of the roughness upon 
the variation, in other words to determine m asa function of both 
nand R. 
(3) In channel investigations it is to be hoped that the triangular 
shape will be adhered to throughout: the law of flow may then 
be discovered, and the influence of form constituted a subsequent 
subject of inquiry. 
In conclusion I wish to say that the main object of this paper 
has been to indicate a scheme of empirical analysis of, and to 
develope a type of formula for, the flow of water in pipes and 
channels, especially the former, rather than to determine, with the 
last degree of possible precision, the constants of the formula itself. 
By means of tables the general expression supplied, can be rendered 
easy of manipulation for the purposes of practical calculation. Its 
general factor gp/8y,, is based on the deductions of rational 
mechanics, and the empirical constants supply the apparently 
hopeless defect which inheres in the complete mathematical solu- 
tion of the problem. That there must necessarily be variations 
of the constants from time to time, as more exact experimental 
data come to hand, goes without saying. If a formula free from 
systematic misrepresentation of the observations has been educed, 
the object of the investigation has been completely attained : itis 
believed that the formula supplied will be found capable of being 
so adjusted, by giving proper values to its constants, to the results 
of new and more exact experiments, that is to say it is substantially 
a general formula. 
Added 24th December, 1897. 
A further reduction, see Table A.—by applying formula (35) 
and assuming m=1 27 of the values of log &, gave for the con- 
stant in (39) § 18 the value 0-248 instead of 0-256. The plot of 
values of log k,. with interpolations for radius (/) and for rough- | 
ness (n) gave very little indication of a variation of m with R 
itself. More accurate experiments are needed. 
University of Sydney. 
