218

FLUIDITY AND PLASTICITY

which would restore the body to its original shape if it were
perfectly elastic, as soon as the stress was removed. On the
application of the stress, the restoring force is first zero, then
gradually increases to a maximum, when at last the flow causes
the strain to disappear as fast as it is produced.

The elasticity e of a solid may be calculated, according to
Morris- Airey (1905), from the fundamental formula

ds = eFdr (74)

where ds is the distance which one plane of the material is sheared
in reference to another plane which is separated from it by a
distance dr, each being subject to the shearing force F. Morris-
Airey has applied this formula to tubes of circular cross-section
filled with gelatine and obtained the rigidity1 £ which is the
reciprocal of the elasticity

where V is the volume of the temporary deformation. It is
assumed that the solid is incompressible. The analogy of this
formula with that of Poisuille is striking.
THE METHODS FOR MEASURING THE FRICTION AND
MOBILITY
To determine the two quantities, friction and mobility, which
go to make up the plasticity of a material, i.e., to locate the curve
in Fig. 77, it is necessary to make at least two measurements of
the flow, using different stresses. We may use the tube method
(Bingham (1916)), the torsion method (Perrott (1919)), or we
may observe the flow in a rod under traction or torsion, the
flow of a cylinder under axial compression, the rate of bending
of a horizontal beam of the material under its own weight, or the
flow of a freely descending stream of material, (Trouton and
Andrews (1904)). Still other methods have been suggested
such as the rate of decay of vibrations in solid bodies, (Kelvin
(1865) and others).
The friction is most easily obtained by the graphical method,
PR
plotting the rates of flow V/t, against the shear, F = ~^r and
1 The assumption which is sometimes made that the rigidity is the re-
ciprocal of the mobility is incorrect.