VISCOSITY OF WATER BY THE EFFLUX METHOD. 97 
in September 1860, in his Introduction to Hemodynamics, the 
development being credited, as I have previously said, to Neumann, 
whose formula may be written in our notation,’ m however being 
assigned the value unity, 
gh = mU*+ 
8 7 
OR 
h denoting the pressure at die entrance to the tube expressed as 
height of a column of liquid of the same density as the effluent, 
and U the mean velocity in the transverse section. Couette was 
evidently unacquainted with Neumann’s or J acobson’s work, but 
in this respect he is not singular.” 
Boussinesq? has attacked the problem with greater rigour, and 
—while admitting that Couette’s solution, which is the same as 
Neumann’s, is legitimately derived, and to a first approximation 
is accurate—shews that a higher approximation gives for m the 
value 1:12. Thus according to the several authorities mentioned, 
m = 0:50 Reynolds (after Bernoulli) 1883 
m = 0°79 Hagenbach oe ... 1860 
m = 1:00 Neumann prior to ... 1860 
m = 1:00 Couette ... ies ... 1890 
m = 1-12 Boussinesq Kae “4 nee 
Poiseuille’s series of measurements, at different pressures and at 
10° C., for a number of tubes afford a means of ascertaining the 
value of this coéfficient for each series : and it may be remarked 
that, a priori, one would expect the deduced values, if not identical 
with, to be somewhat greater than Boussinesq’s coéfiicient, inas- 
much as it is said that the tubes retaining their cylindrical form 
a eee 
: } Archiv. fur Anat. und Phys. Reichert’s, 1861, p. 321. Jn the original 
— both sides of this equation is multiplied by 2. 
That Hagenbach’s correction should have been so invariably 
used, is 
‘in itself an indication of how little is generally known of Neumann’s fine 
exposition of the theory of flow in a tube. 
rere Rendus, t. 110, p. 1160—1166, et p. 1238 - 1242, 1890. Ibid 
18, p. 9-15 et p, 49 ect. 1801. ‘Théorie du régime permanent gradu- 
filets varié qui se produit prés de l’entrée évasée d’un tube fin ot les 
@un liquide qui s’y écoule n’ont pas encore me lour inégalités. 
Bormales de vitesse, etc, 
G—July 3, 1896, 
