  We present a model of a slowly rotating Tolman VII (T-VII) fluid sphere, at
second order in the angular velocity. The structure of this configuration is
obtained by integrating the Hartle-Thorne equations for slowly rotating
relativistic masses. We model a sequence in adiabatic and quasi-stationary
contraction, by varying the tenuity parameter $R/R_{\mathrm{S}}$, where $R$ is
the radius of the configuration and $R_{\mathrm{S}}$ is its Schwarzschild
radius. We determined the moment of inertia $I$, mass quadrupole moment $Q$,
and the ellipticity $\varepsilon$, for various configurations. Similar to
previous results for Maclaurin and polytropic spheroids, in slow rotation, we
found a change in the behaviour of the ellipticity when the tenuity reaches a
certain critical value. We compared our results of $I$ and $Q$ for the T-VII
model with those predicted by the universal fittings proposed for realistic
neutron stars. For the relevant range of compactness, we found that relative
errors are within $10\%$, thus suggesting the T-VII solution as a very good
approximation for the description of the interior of neutron stars.
