STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 339 
15. Reynolds’ theory that U" « N- R* inconsistent with 
experiment.—Reynolds’ general formula (7) may, by putting M’ 
for MU f*, be written 
Bi fas 
BS: tial femal se > (30) 
from which it is evident, by taking logarithms, that 
E=log k" —(3-~n) log. R = log M’ —log N(n).........44 (31) 
a linear equation. 
The values of é can be formed from Table A. ; if then they be 
plotted as ordinates and the corresponding values of n as abscisse 
the result will evidently be a straight line, provided Reynolds’ 
formula be correct. The values of € arranged in the order of 
increase of n are as hereunder, the number above denoting the 
horizontal line in Table A. 
Table F. 
Calculated values of € by (31). 
Jans Table A, i 3° ER 6 UU Sh U8 
100 € = 463 466 464 460 463 467 474 468 468 475 
Line ia TS 1S A 16+ I ae 
100 € = 450 480 481 479 463 501 504 506 488 470 
It may be supposed that the required linear relation would more 
conspicuously appear, if the means of a large number of observa- 
tions be taken. In order to test this also, the mean results of the 
bottom of Table G. hereinafter, are used for the evaluations of é¢. 
The results arranged in order of n are 
100% = 179 185 186 188 189 190 191 
100 € = 465 468 481 471 481 485 475 
Neither of these series represent a straight line, nor do they 
indicate any law of progression whatsoever. Reynolds’ theory of 
the variation of velocity with the radius of the pipe is consequently 
shewn to be inconsistent with the results of observation ; and his 
assertion that his general formula holds for all pipes and all veloci- 
ties, proved to be without sufficient justification, As his formula 
is purely empirical, inconsistency with experiment is a sufficient 
