82 G. H. KNIBBS, 
Hagenbach’s! memoir was published in March 1860. He 
deduced the general formula for flow in indefinitely long narrow 
tubes of circular section, in which the velocity is zero at the sides | 
of the tubes, and considered the fall of pressure occurring at the | 
entrance of the tube, for which he furnished a formula. This | 
formula, though somewhat inexact, has been used for correcting 
observed differences of pressures, at the tube terminals, by nearly 
all subsequent observers. 
Almost contemporaneously with Hagenbach’s memoir, the date : 
of publication being but one month later, the results of Helmholtz’ 
and Piotrowski’s? researches appeared, the latter dealing with the | 
experimental, and the former with the theoretical side of the 
subject. In their joint memoir Helmholtz developed an expression 
for flow in narrow tubes of circular section intrinsically identical | 
as regards its first term with Hagenbach’s, but containing 1 
addition a second term representing the influence of friction ab j 
the boundary of the flowing liquid. This Helmholtz and his : 
colleague deemed necessary in a complete formula, in view of the 
fact that their experiments pointed to the existence of a relative 
movement and’ consequent frictional effect at the boundary com 
mon to the liquid and the containing vessel, at any rate as betweel 
a polished gilt surface and water, and their formula is substantially 
identical with the earlier formule of Neumann or J acobsom 
Neither Hagenbach wor Helmholtz refer to any earlier corte 
expression for steady rectilinear motion in pipes of circular sectio! 
and it is somewhat remarkable that it is generally credited tot 
latter, although so far as I can ascertain, Stokes, Neumann, 
Hagenbach all have a prior claim to this credit. A second 4 
very valuable discussion by Jacobson? of the theory of rectilineat 
flow and evaluation of viscosity was communicated in Septe”t 
ay Ueber die Bestimmung der Zihigkeit einer Fliissigkeit durch de? 
Ausfluss aus Rohren. —Pogg. Annal. Bd. 109, p. 384 — 426, 1860. 
* Ueber prise. sesganiel Flissigkeiten—Sitzber. k. k- aia 
‘Wien., Bd. 40 sag 
3 Zur Bialng in die a anena —Archiv. fiir Anat. und Page| a 
1861, p. 304 - 
