226 FLUIDITY AND PLASTICITY
stress somewhat above the friction, so we have no idea as to how
the value of e may vary with the rate of shear, and the equation
becomes unmanageable. .Fortunately by using the higher rates
of shear we can apparently always obtain the simple linear
relationship. If later experiments prove that this is not the case
it will be time to use the more complex formulas.
The Traction Method.—Trouton has discovered that the rate
of flow in a rod of material subjected to traction is not propor-
tional to the tractive force T, but analogously to Eq. (73)
dv = \(T - t)dr (90)
where X is the coefficient of plastic traction, and t is a tractive
friction constant. The value of t may be found by plotting
the elongation dv/dr against the tractive force and extrapolating
the curve to the axis. Trouton has obtained values of X for
pitch of 2.3 X 10~10 and for shoemakers' wax of 1.7 X 10~7. To
obtain the relation between the coefficient of plastic traction and
the mobility, we note that the tractional force applied to a rod
may be resolved into two equal shearing stresses at right angles
to each other and at 45° to the direction of traction. The value
of either shearing stress is one-third of that of the tractive stress,
hence the friction is one-third of the tractive friction and the
mobility is one-third of the plastic traction coefficient as shown in
Table LX.
The Torsion Method.—Trouton applied a constant torque
to the ends of a cylinder or tube of substance and observed the
relative motion of the ends. He found that rods which were
carefully made could be twisted almost indefinitely, provided
that they were maintained in a horizontal position. The motion
was fastest when the stress was first applied but the angle of
twist per unit length U soon became a linear function of the time.
Conversely when the stress was removed, the bar started to
twist in the opposite direction. He made the experiment of
removing weights at such a rate that the rod would not move in
either direction, and found that the weights remaining were
inversely proportional to the time elasped. This kind of elastic
recovery was found to be present in glass and sodium stearate.
Trouton does not seem to regard his materials as solids but he
makes it very clear that the angular velocity is not directly pro-