STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 341 
the slope index and of log k” so deduced are,— 
Mean n (a) 1°783 (6) 1882 (c) 1:948 
no log eo OSS 5:162 5145 
The differences from the mean—5-146—are too small to lend much 
force to the supposition of an increase of k” with n, though 
undoubtedly such a supposition would minimise the inconsistency 
between theory and experiment so far as these three values them- 
selves are concerned. It will also later appear that there is @ 
sufficient reason for regarding k” as increasing with n. 
s 4 s 
If with several series of pipes—each with surfaces identical in 
character, but different in the different series, and each series 
comprising pipes of identical radii but covering a wide range— 
one could obtain results shewing either no variation, or a systematic ~ 
variation of m with the radius of the members of each series, the 
problem of finding the relation of &” to the radius would be simple. 
But the anomalous nature of the results in regard to n, shewn in 
Table A.,:and in regard to k”, shewn in Table G., make it clear 
that a completely satisfactory solution is impossible with the 
existing experimental data, and one is inclined to dismiss the 
matter as hopelessly enigmatical. 
There are, however, three ways in which these tabulated results 
may be tentatively examined. We may (i.) either take pipes of 
the same category with values of 7 as nearly as possible identical, 
and see whether the law of variation of k” with R, changes 
systematically with the category itself: or (ii.) we may select 
pipes of any description with the same radius, and from the mean 
values of k” (or of some other function thereof) endeavour to 
ascertain for each series with that radius, the variation of 4” with 
F, supposed in such a case to be quite independent of the category, 
and therefore also of the magnitude of , the mean value of which 
varies with the category : or yet again (iii.) we may endeavour to 
ascertain whether the variation is one that involves 2 itself. 
First as regards method (i.):—Since the loci of points, whose es 
logarithmic codrdinates are k’ and R, give indications of being at : 
