Uniformly varying stress:  

Let a prism of incompressible elastic material be subjected to gravitational pull, so that it is subjected to the following body forces,

(3.24)

Then all the stress components vanish, except which from equation 2.12 is obtained as

(3.25)

The strain are given by the equation,

(3.26)

To displacements can be obtained in the following manner,

,

which gives

(3.27)

From , we have,

(3.28)

which on integration results in,

Then,

(3.30)

Hence,

and

(3.31)

The equation results in

(3.32)

The above equations signify that should satisfy the following equation

(3.33)

where are constants.

The equations containing show that is a function of , say and is a function of , say . Hence, and can be of the form,

and

(3.34)