STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 319 
facilitate either natural or logarithmic computation. The table 
is based upon the assumption that the viscosity at 10° O. is 
0-013107, and that the relative fluidity at that temperature is 
1-365, that at 0° being unity, », is consequently 0-017891. 
The following supplementary table of values of the fluidity from 
40° to 100° C. is based on the mean of Slotte’s (1883) and Thorpe 
and Rodger’s (1894) values. These have been so adjusted that 
the differences progress regularly, but since Slotte gives for the 
higher temperature 5-983 and Thorpe and Rodger 6-282, the 
fluidity must be considered as very uncertain for the higher tem- 
peratures.! 
TABLE II. 
Temp. r. 40°C.. 45 50 55 60 65 70 
Fluidity 7. 2-72 2:97 3:23 350 3-77 405 4:34 
Log. f. +435 473 509 544 576 607 637 
Temp. 7 70. 80° 86 a TO 
Fluidity f. 463. 4:92 5:22 552 5°82 6:13 
Log. f. -666 692 -718 -742 -765 ‘787 
5. Instability of rectilinear flow in pipes.—It has long been 
known that the circumstances of the motion of water in pipes 
and channels are subject to characteristic differences, the general 
cause of which was indicated by Stokes in 1842.° Hagen in 
1853, while investigating the influence of temperature,’ distinctly 
1 See Journ. Roy. Soc. N.S.W., Vol. xxx., p. 193, 1896. 
? On the steady motion of incompressible fluids—Trans. Camb. Phil. 
Soc., Vol. vit., pp. 434-454 and 465, 1842. On the analytical condition 
of the rectilinear motion of fluids ete.—Phil. Mag. Vol. xx1., pp. es 
300, 1842, and Vol. xx11., pp. 55, 56, 1843. 
3 Ueber den Einfluss der Temperatur auf die Bewegung des Wassers 
in Rohren.—Abhandl. Akad. Wiss. Berlin, 1854, Math. Abt. pp. 17. The — 
Paper was read a Nov., 1853. The following passage illustrates the 
point :— Hieraus ergiebt sich, dass die innern Bewegungen sich bilden, 
~ Laster sehr stark zunehmen, sobald die Geschwindigkeit das 
nna 
weiterer tate des W. Wasners sich nicht ‘vergrossern 
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