  In this work, we investigate the correspondence between the Erez-Rosen and
Hartle-Thorne solutions. We explicitly show how to establish the relationship
and find the coordinate transformations between the two metrics. For this
purpose the two metrics must have the same approximation and describe the
gravitational field of static objects. Since both the Erez-Rosen and the
Hartle-Thorne solutions are particular solutions of a more general solution,
the Zipoy-Voorhees transformation is applied to the exact Erez-Rosen metric in
order to obtain a generalized solution in terms of the Zipoy-Voorhees parameter
$\delta=1+sq$. The Geroch-Hansen multipole moments of the generalized
Erez-Rosen metric are calculated to find the definition of the total mass and
quadrupole moment in terms of the mass $m$, quadrupole $q$ and Zipoy-Voorhees
$\delta$ parameters. The coordinate transformations between the metrics are
found in the approximation of $\sim$q. It is shown that the Zipoy-Voorhees
parameter is equal to $\delta=1-q$ with $s=-1$. This result is in agreement
with previous results in the literature.
