342 G. H. KNIBBS. 
least very nearly straight lines, it may with propriety be assumed 
that, very approximately, 
pe S R™ (32) 
whence log k” = log k' +m log R......... (33) 
and consequently if &’ be constant 
m = oF eS LS OA. (34) 
Should there be a small variation of m with R, it will appear in 
the changing values of m, as the values of the radius are changed. 
The results of the application of this last formula, viz., (34) are 
shewn in Table H. 
Seng Table H. 4 
Table A. ee, sicacuanis waelaudin eayuttas. Cale. Mean 
1— 2 1-700 Lead, Reynolds 1:30 1:39) «ee 
46° 1-771. 4, Darcy 1:23 191, ee 
BIG fo pee 4g 1-22 0:84 1-02 
$4.0: VIO js a 1:22 0-98 1°37 
7— 9 1-775 Tarred Iron, Darcy 1:21 1:30 5°57 
8-10 1-805 o = 1:19 109 919 
11-13 1-841 Drawn Iron, _,, 1:16 1:74 «1°29 
12-13 1:867 . : 1:13 1:24 1°65 
15-16 1-927 New Cast Iron, ,, 1-07 114 812 
14-16 1-947 ‘ ‘3 1-05 1:04 675 
18-20 1-983 Incrusted Iron, ,, 1-02 1:23 6:98 
Means 1-834 1166 120 40l 
The values of m in the table do not afford definite evidence of 
a regular variation either with the value of n—a conclusion pre 
viously reached—or with the class of pipe. Further, the absence 
of any systematic relation between m and 3 — n indicates the pro- 
priety, if not of wholly rejecting Reynolds’ relation, at least of 
regarding it as not yet proven. 
To test the next method, (ii.), we resort to graphics, using the 
mean values of log &” given in Table G.: the result is shewn in 
Fig. 8, and gives as a mean value for m, 1-27; while the mean 
value of n is 1834, whence 2—n=1-166, The difference though 
