  I derive a relation, both `forward' and `inverse', between the density and
the divergence of the peculiar velocity which results from the Zel'dovich
approximation. My calculations assume Gaussian initial conditions. The forward
relation expresses the density (strictly speaking, the expectation value of the
continuity density given the velocity divergence) in terms of the velocity
divergence, while the inverse relation expresses the velocity divergence in
terms of the density. The predicted scatter in the relations is small, hence
the inverse relation is close to, though not identical with, a mathematical
inversion of the forward one. The forward relation is equivalent to the
well-known `standard' density--velocity relation in the Zel'dovich
approximation. The inverse relation, however, is successfully derived for the
first time and constitutes a potentially interesting alternative to an inverse
relation derived by Chodorowski et al., based on third-order perturbation
theory. Specifically, it may better recover the peculiar velocity from the
associated density field, when smoothed over scales as small as a few
megaparsecs.
