STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 325 
in which h is the resistance head, and & is a coéflicient varying, 
for the one class of pipe, only with the temperature: he gives 
values of the coéfficient &.1 
This in 1853. It is remarkable therefore to find Reynolds in 
1883, asserting without qualification, that no previous experimenter 
had discovered the law J « U "and that without exception they 
had employed either the relations J « U?,orl «x (7+ BU), 
St. Venant in 1850 mentioned? that DuBuat had long ago observed 
that the exponent » was too great (probably in the latter’s 
Principes WVhydraulique, Paris 1786). In 1869 Hagen referred 
to the fact® that Woltmann had first employed the expression n= £ 
—doubtless toward the end of last century—and also that _ 
Eytelwein' had used #4 or 2, which latter, he says, Darcy accepted 
while St. Venant selected 42. Even as far back as 1850, St. 
Venant? employed the graphic method of plotting the logarithms 
of the related quantities, by which means he said, the conviction 
that the variation is as U ™ (nm being less than 2) was easily 
reached, and he assigned the values-?4 for canals and + for pipes. 
He moreover clearly perceived the state of turbulent agitation 
(“Tétat torrentueux” p. 583), and its signal influence upon the 
coéfficient of internal friction.® In 1872 he described the state of 
i Loe. cit., p- 86. 
2 His words are :—“ bien que cette expression ” (viz U*) “ soit cua 
‘i Sr ce eee: Vexpérience a appris et fait dire depuis longtemps a a Byet 
3 Usb ber die Beweging des Wassers, etc. = Aphand. Akad. Berlin 1869, 
(2) Math. Teil. pp. 1-29. See in particular 
4 Bemis sur des formoules, nouvelles gas te solution des a 
relat; 
tJ 
ais 
bene: deux suites des points ayant pour ‘ghecieies les walen de 
* Sur Phydrodynamique des cours Vea aaa maw t. 74, PP. : 
570-577, 649 - 657, 770 —774, 1872. 
