  The fourth order Weyl gravity theory of Mannheim and Kazanas is based on
replacing the Einstein-Hilbert action with the square of the Weyl tensor, and
on modifying the matter action of the standard model of particle physics to
make it conformally invariant. This theory has been suggested as a model of
both dark matter and dark energy. We argue that the conformal invariance is not
a fundamental property of the theory, and instead is an artifact of the choice
of variables used in its description. We deduce that in the limit of weak
fields and slow motions the theory does not agree with the predictions of
general relativity, and is therefore ruled out by Solar System observations.
