  Einstein's traceless 1919 gravitational theory is analyzed from a variational
viewpoint. It is shown to be equivalent to a transverse (invariant only under
diffeomorphisms that preserve the Lebesgue measure) theory, with an additional
Weyl symmetry, in which the gauge is partially fixed so that the metric becomes
unimodular. In spite of the fact that this symmetry forbids direct coupling of
the potential energy with the gravitational sector, the equivalence principle
is recovered in the unimodular gauge owing to Bianchi's identities.
