AMPLIFICATION OF THE LAW OF POISE UILLE

Since the values of K are unity within the experimental error
to the length is zero. In no single instance does
of A amount to even one-half the diameter of the tube.
however the value of m had been taken as unity, A would
appeared to have positive value.

Had A been found to have a definite value, it would
boen necessary to consider the legitimacy of making the correc-
tion by means of an addition to the length of the capillary instead
of by means of a correction in the pressure as suggested in Eq. (2)
fo-ut since no definite value can be assigned to this correction
there is no need for raising the question.

The shape of the ends of the tube are of considerable irnpoir-
tan.ce in determining the development of turbulent flow, under coir-
tain conditions. Tubes with trumpet-shaped entrances appear to
promote linear flow (c/. Reynolds (1883) and Couette(1890) p. 48€>).

Slipping.—-Coulomb (1801) made experiments with an oscilla-fc-
ing disk of white metal immersed in water, and he noted ttta^t
coating the disk with tallow or sprinkling it over with sandstone
h_ad no effect upon the vibrations. This seemed to prove that "bite
flizid in contact with the disk moved with it, and that the proper-ty
b-oing measured was characteristic of the fluid and not of ttte
jxa/ture of the surface. These observations were confirmed
O. Meyer in 1861.

After the Law of Poiseuille had been experimentally
theoretically established, it was still unsatisfactory that ttie
results of measurements of viscosity by the efflux method did
n_o"fc agree with those by other methods. It was natural tx>
sxippose that the discrepancy might be explained by the
friction between the fluid and the solid boundary which had
assumed by Javier (1823), cf. also Margnles (1881) and Hada-
mard (1903). Helmholtz in his derivation of the Law of ]Pol-
seiiille had taken into account the effect of slipping ajad obtained
tlie formula, -which in our notation is

V = + 4>J&« (13)

wh.ere X depends upon the nature of the fluid as well as upon
of the bounding surface. In treatises on hydrodynamics this Is
written