VISCOSITY OF WATER BY THE EFFLUX METHOD. 89 
which has been experimentally justified between somewhat wide 
but ill-defined limits. 
6. Coéfficient of sliding friction for glass and other tubes.— 
Navier assumed that a flowing liquid would glide or slip with a 
finite velocity at its bounding surface, and Piotrowski’s experi- 
ments—by method (d) § 1—interpreted by Helmholtz,” confirmed 
this view to a limited extent, for although there was no slipping 
in the case of ether and alcohol in contact with polished gilt 
surfaces, with water and some other liquids slipping apparently 
occurred, and values for the coéfficient were deduced.® Piotrowski’s 
experiments did not include cases of flow through tubes under 
pressure, but Helmholtz, after developing the theory of Piotrowski’s 
method, turned his attention thereto, and deduced the formula to 
which we have already referred. He concluded from an examina- 
tion of Girard’s observations that sliding friction, the assumed 
existence of which seemed to explain Piotrowski’s results, must 
also be postulated in the case of flow through tubes, at any rate 
when their dimensions were somewhat larger than those used by 
Poiseuille, and when they were of copper instead of glass. He 
further deduced a value for his coéfficient 6—in our first equation 
—by applying the formula on the assumption that the motion 
might be deemed steady.* 
The legitimacy of these conclusions was questioned by Whetham 
in 18905 who judged, from his experiments by an efflux method, 
that no slip occurs, at any rate in the case of surfaces which are 
wetted by the liquid. But Brodmann—in 1892—has demon- 
_ Strated, I think beyond doubt, that water in contact with a gilt 
surface does not adhere thereto and that under such circumstances 
‘siege oC eae na kes aa BBE SE ge ee eee a ree ne a 
L Mém. de l’ Académie, t. 6, p. 389. 
* Sitzber. Akad. Wien., Bd. 40, p. 607 - 658. 
3 Loc. cit., p. 621. 
* Thid, p. 656, where = b in the equation previously given. 
5 On the alleged slipping at the boundary of a liquid in motion. 
Trans., Vol. 181, p. 559. 
* Thid, p. 582. 
—Phil. 
