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IX. On the Alleged Slipping at the Boundary of a Liquid in Motion. 
By W. C. Dampier Whetham, B.A., Coutts-Trotter Student of Trinity College, 
Cambridge. 
Communicated by J. J. Thomson, M.A., F.B.S., Cavendish Professor of 
Experimental Physics, Cambridge. 
Received June 7,—Read June 19, 1890. 
In treatises on hydrodynamics, the flow of a liquid through a straight tube is investi¬ 
gated on the supposition that there may be finite slipping between the walls of the 
tube and the outermost layer of liquid. This leads to the introduction of a “ slipping 
coefiicient ” which vanishes when there is no relative motion between them. 
Let r denote the radius of the tube, 
Pi the pressure at one end, 
p^ ,, „ the other, 
[i the coefficient of viscosity, 
I the length of the tube, _ 
p the density of the liquid. 
Then it may be shown (Lamb’s ‘ Hydrodynamics, p. 222) that when the motion is 
linear the flux is given by 
J ttA Pi - 2B lUf Pi - Ih 
^ fip I ^ /3 I 
1 
8 
-^(Pl -Pj) 
ppl 
+ 4/xp^ 7-3j, 
' where l/y8 may be defined as the slipping coefiicient. 
The experhnents of Poiseuille'" showed that the coefiicient was certainly zero for 
glass tubes, but there was doubt whether this held for all materials. 
Helmholtz and PiOTROWSKit attacked the problem in another way. They sus¬ 
pended bifilarly an accurately worked sphere, whose inner surface was gilded and 
polished, and by observing the time of swing and the logarithmic decrement when 
the sphere was filled with water and various other liquids, deduced a value for the 
* ‘ Memoires cles Savants fltrangers,’ 1846. 
t ‘ Sitzungsber. der k. Akad. in Wien,’ vol. 40, 1860. 
7.10.90 
