. 
340 G. H. KNIBBS. 
reason for its rejection : other considerations indicated in the next 
section, will lend a still stronger sanction to its abandonment. 
16. Proof that the parabolic relation U® « R™ is experimentally 
justified for flow in pipes.—In order to ascertain whether the 
variation of velocity with the radius of the pipe, depends also on 
the index n already found—though not in the way stated by 
Reynolds—and generally to see at a glance, if possible, the relations 
of k” and R, the following table, shewing the values of ky, for 
different pipes of the same radius,’ was formed from the results 
given in Table A: The quantities marked * are taken directly; 
the others are logarithmically interpolated from the nearest 
quantity, after ascertaining that the logarithmic homologues, the 
.coérdinates of which are log &” and log #, do not appreciably 
differ from straight lines. Since the interpolations are small, this 
process is not illegitimate. 
Table G. 
mabea. ™ LogR Logk, Pipe. lmiea, ™ Log R Logk, Pipe. 
1710 9°845 4460 Lead 8 1:808 0612 5°475 T. Iron 
401784. 4. 4666 ,, 14% 1957 ,, 5693 C. Iron 
11 1828 ,,- 4369 D.Iron |19 1 » 6808 I. C. Iron 
4 1768 0127 4792 Lead 9 1778 0-973 5861 T. Iron 
7e1769 = 757 T.Iron |16 * 1:9 » 6069 C. Iron 
12° 1879, Ss: 4928 -~D. Tron (20 1-982 ,, 5°842 I.C.Iron 
18 1985 ,, 4817 I.C.Ironj10 1-803 1-085 5:987 'T. Iron 
5 1775 0296 4599 Lead [16 1°988 ,, 6:158 ©. Iron 
131855 ,, 651388 D. Iron (2021-982 ,, 5980 I.C.Iron 
18' 1°985 seh 5005 I.C.Ironj/l7 1°861 1:398 6-404 C. Iron 
Values of R 0-70; 1:34; 1975; 4095; 9-40; 12:16; 25:0 
Mean log k” 4-461; 4823; 5°046; 5-492; 5-924; 6042; 6-404 
Mean n 1-774; 1850; 1872; 1891; 1-899; 1-908; 1-861 
The table shews many anomalies, but indicates clearly, of course, 
an increase of k” with R. In order to find whether there is any 
evidence of a progression of the value of k” with n, the sums of 
_ lines, with approximately the same value of n, are taken from 
each radius series. These summations are (a) 3.$+7.5.8.- 9; 
(b) 11.12.13.19.16; (c)11.18.18’.14.20, The means of 
Gp aes 
1 The suffix 14 denotes that the value of k’ is for a temperature of 14°C- 
