  A new tensor $D$ is introduced which is constructed from the Lanczos
potential and is of the same form as that of the Weyl tensor $C$ expressed in
terms of the Lanczos potential except that covariant differentiation is
replaced by transvection with a vector $v$. The new tensor has associated
invariants $C\cdot D$ and $D^2$, the first of these can be interpreted as a
Chern-Simons term for Weyl $C^2$ gravity. Both invariants allow various tensors
to be constructed and some of the properties of these are investigated by using
exact examples.
