  We present a calculation of the Casimir torque acting on a liquid crystal
near a birefringent crystal. In this system, a liquid crystal bulk is uniformly
aligned at one surface and is twisted at the other surface by a birefringent
crystal, e.g. barium titanate. The liquid crystal is separated from the solid
crystal by an isotropic, transparent material such as SiO$_2$. By varying the
thickness of the deposited layer, we can observe the effect of retardation on
the torque (which differentiates it from the close-range van der Waals torque).
We find that a barium titanate slab would cause 5CB
(4-cyano-4$'$-pentylbiphenyl) liquid crystal to rotate by 10$^\circ$ through
its bulk when separated by 35 nm of SiO$_2$. The optical technique for
measuring this twist is also outlined.
