STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 337 
from which g appears to be about 0-274. The consistency of the 
results is not quite equal to Hagen’s. See Fig. 7 (0). 
Again, Unwin,’ in his experiments on the friction of discs 
rotating in water, obtained results which indicated that the 
moment of resistance u of the disc, varied as the 1:85 power of 
the rate of revolution, V say: that is cw =V% His experi- 
ments treated as above give 
Table D 
Temp. Celsius o"F Lae 21:3 54:7 
Value of log f 071 "155 262 542 
Value of log c’ «+°914 ‘939 ‘955 1-000 
_ from which the value 0-170 is deduced for g. See Fig. 7 (c). In 
these three instances there is no indication of any systematic 
departure from the relation, which we set out to test, viz. J"« f%. 
13. Reynolds’ supposed law, that q=2-n, not experimentally 
justified. Reynolds’ formula (7) § 6 herein, asserts that Us f?-" 
which leads to this very remarkable result, viz. that when the 
roughness of the channel. involves the velocity-and-‘slope’ relation 
U2 & 2, temperature has no influence on the flow, as remarked by 
Lord Rayleigh,* and as is immediately obvious from the formula 
itself. Moreover if m should exceed 2, increase of temperature 
and the consequent increase of fluidity would actually diminish 
the flow. I this be so, it is necessary to suppose that the general 
decrease of the resistance to tangential stresses and consequent 
acceleration of velocity is more than compensated by the quantity 
of internal agitation facilitated by this decrease itself. Since 
there is no reason to regard the condition as unstable, such a 
supposition seems in opposition to the law of least action, and 
to be wholly improbable. It is not very clear from Reynolds’ — 
paper, on what experimental, to say nothing of theoretical, grounds 
he justifies a formula leading to such remarkable consequences. 
Peemining it in the light of the results reached in last section, we 
1 Flow of Water &¢.—The Engineer, Vol. uxt, p. 1, Jan. 1886. _ 
? See Phil. Mag. Vol. xxxrv., 1892, PP: . 59 = ~ 145 - 154, 177 - 180. 
V—Dee. 1, 1897. : 
