68

FLUIDITY AND PLASTICITY

if;

amount of liquid may flow into V from E after the record of the
time has begun, and this will tend to offset the effect of any liquid
left in V at the end of the time of flow. To make these amounts
as nearly equal as possible, the lower part of E should be exactly
similar in shape to the lower part of V.
The pressure should be variable at will so that the time of
flow may be kept reasonably constant. For gases, high pressures
are as unnecessary as they are undesirable. For incompressible
fluids, there need be no upper limit set to the pressure. A pres-
sure of 50 g per square centimeter can easily be read to 0.1 per
cent on a water manometer, and the various pressure correc-
tions—to be discussed—may be ascertained well within this
limit, hence this may be taken as a lower limit.
The measurement of the radius of the capillary offers the great-
est difficulty in viscosity measurement by this method. Since
the flow is proportional to the fourth power of the radius, any
error in this measurement is multiplied four times. Careful
weighing of the quantity of mercury required to fill the tube is
perhaps the best means for obtaining the mean radius, R =
-\/(W/irpl); but for a capillary such as that used by Thorpe and
Rodger, Z = 4.94- cm R = 0.0082-I- cm, the weight of the mer-
cury is only about 0.013 g so that the desired accuracy is diffi-
cult to obtain with the ordinary balance. If the radius is
increased, the time of flow may be kept constant by increasing
the length so that the ratio l/R4 is constant. Fortunately both
of these changes tend to increase the volume of the capillary.
At the same time the increase in length diminishes the effect
of any possible alteration in the stream lines near the ends; and
the increase in the radius diminishes the possible effect of slip-
ping and probably also the effect of dust particles.
The formula (20) applies only to a capillary which has the
form of a true cylinder, but usually the capillary is elliptical and
it may at the same time be conical. To determine the conicity,
the tube must be calibrated with a mercury thread. To deter-
mine the ratio of the axes, the micrometer microscope should
be used. In using the micrometer microscope it is somewhat
difficult to see the exact circumference to be measured, owing to
various causes. Poiseuille found it best to grind off and polish
the end of the tube and then attach a cover-slip to this end by