560 
MR. W. C. D. WHETHAM ON THE ALLEGED SLIPPING 
coefficient of viscosity and for the slipping coefficient, from the theoiy of spheres 
oscillating in a viscous medium, as wo]'kecl out by Stokes and Helmholtz, 
For distilled water their value of the factor /xp in the above expression is 
X = 2‘3534 mm. 
If we apply this to the case of a tube we get a somewhat startling result. From 
equation (i.) it follows that the effect of slip varies inversely as the radius of the tube. 
The smallest tube practicable in the experiments to be presently described had a 
diameter of about a millimetre. It is easy to show that the result of the existence of 
a slipping coefficient of the magnitude given by Helmholtz would be to produce an 
increase in the volume of liquid flowing through the tube in a given time, which could 
not only be detected, but would be of such importance that it could not easily be 
masked. 
In Helmholtz’s notation equation (i.) is written 
iTlih_M I 4x^.3 1 
the density of water l^eing taken as unity. 
Putting r = ’05 and X = '23534, we get 
1 (Pi - Ih) 
X 117-67 X 10“*^; 
“ fjil 
whereas if there is no slip, so that X vanishes, the flux becomes 
X 6-25 X lO-'*’. 
If we take Helmholtz’s coefficient to be correct, the flow through a polished gilt 
tube of a millimetre in diameter is nearly twenty times as fast as through a glass 
tube of the same size. 
Helmholtz refers to some experiments made by Girard with copper tubes* which 
make the flow some four times faster than do Poiseuille’s formulge. I shall return 
to the consideration of these observations later. The value of X which Helmholtz 
deduces from them is 0'3984 mm. 
The discrepancy between these results and the generally received opinion that no 
slip occurred with any material seemed worthy of further investigation. 
It is evident tlrat the alleged coefficient could be investigated with much greater 
advantage by observing the flow of liquid through a small tube than by any experi¬ 
ments on oscillating spheres. In order to avoid all absolute determinations while 
searching for the existence of such a slip, I decided to observe the time of flow of a 
* ‘ Memoires de ITnetitufc,’ 1813-1815. 
