VISCOSITY OF WATER BY THE EFFLUX METHOD. 81 
friction, gave I believe, the first rational interpretation of the law 
of flow in long narrow tubes. 
In 1847 Moritz followed with some observations on Coulomb's! 
method. Seven years later (1854) Hagen” attempted a more 
general solution of flow in narrow tubes, following much on 
Gerstner’s lines. In 1858 Ludwig and Stefan* made an important 
contribution to the theory of this subject, but it was not until 
January 1860, that the viscosity coéfficient appearing in the 
equations of Navier was included in an exact and general formula 
for the efflux from tubes: it then appeared in Jacobson’s* contri- 
bution to haemodynamics. This furnished the results of a some- 
what extensive series of efflux experiments, and gave an exposition, 
credited to Neumann, of the theory of flow in cylindrical tubes of 
circular section. The date of the first publication of this expo- 
sition I have not been able to ascertain, but it must have been 
prior to 1860. It contained an accurate and complete deduction 
of the law of velocity in a right circular cylinder, on the assump- 
tion of a velocity at the boundary of the liquid ; employed terms 
to represent the internal friction and that at the boundary ; and 
showed that when the boundary velocity was zero Poiseuille’s law 
was obtained. It dealt moreover with the fall in pressure at the 
entrance to a tube, basing the formula for its amount on Newton’s 
value for the coéfficient of flow for short cylindrical adjutages. It 
is also worthy of remark that the viscosity is expressed in the 
absolute system in Jacobson’s treatise, and that he experimentally 
showed that the law held for larger tubes than were used by 
_ Poiseuille, 
OEE EEN 
a 1 Einige Bemerkungen iiber Coulomb’s Verfahren, die Cohiision der 
lissigkeiten zu bestimmen.—Pogz. Annalen. Bd. 70, p. 74—85, 1847. 
2 Ueber die Bewegung des Wassers in ges cy ee Rohren.— 
Abhandl. d konigl. Akad. d Wiss. zu Berlin, 1 
ichtung ausiibt.—Sitzber. Akad. Wien., Bd. 32, p. 25 - 42, 1858. 
bate zur Haemodynamik.—Archiv fiir Anat. und Physiol. 1860, 
* Vortriige itber Hydrodynamik. 
F—July 3, 1895, 
