ail oe er Sate = ie Sis a ig EGE AO, Se 
VISCOSITY OF WATER BY THE EFFLUX METHOD. 93 
of water. But apart from such theoretical deductions from 
experiments, it may be noticed that the strong adhesion of the 
bounding film to the tube was visually demonstrated in the 
experiments of Duclaux.!_ We may therefore in dealing with the 
theory of flow in glass capillary tubes, when the motion is recti- 
linear confidently assume that the coéfficient 8 in equation (1) is 
infinite—or in other words that there is no slip—that the velocity 
at the boundary of the section is consequently zero, and that the 
term in &* vanishes, and this assumption will generally be correct 
for any tube whatsoever for steady rectilinear flow. 
LT. The reduced equation of flua.—Denoting by P’ the difference* 
Po —Px, the original equation (1) becomes for zero velocity at the 
boundary 
a formula first given by Neumann, then by Jacobson, Hagenbach,* 
and Helmholtz. If K be substituted for x/(2'y) and D the 
diameter for R the radius, Poiseuille’s formula*— 
inca! “te 
derived experimentally about 1840, is obtained. The earlier 
formule viz. Girard’s (1813), and Navier’s (1822) were erroneous, 
making the efflux proportional to the third instead of the fourth 
power of the diameter. 
8. The determination of the fall in presswre.—In large tubes, in 
which flow is established, the fall in pressure due to viscosity or 
other resistances between two cross sections any distance apart, 
may be measured manometrically, or by observing the vertical 
1 Recherches sur les lois des mouvements des liquides dans les espaces 
capillaires.—Annal. de Chimie, 4 Sér. t. 25, 1872 
? We use P’ instead of P as the latter is hereinafter used to denote a 
Pressure directly observed but subject to certain corrections. 
3 Pogg. Annal. 109, i ‘a is 
p. 397, 400, 401. In our notation ' = 7/9 
Hagenbach’s k/n o 
* Com; hina t. 11, p. 1046, 1840. Mem. des Savants étrang. t.9, 
cara The relations of K, P » for arbitrary or for absolute units are 
to hereafter: here we regard only the form of the expression. 
