  We report inelastic and elastic neutron scattering, magnetic susceptibility,
and heat capacity measurements of polycrystalline sodium ruthenate
(Na$_3$RuO$_4$). Previous work suggests this material consists of isolated
tetramers of $S=3/2$ Ru$^{5+}$ ions in a so-called "lozenge" configuration.
Using a Heisenberg antiferromagnet Hamiltonian, we analytically determine the
energy eigenstates for general spin $S$. From this model, the neutron
scattering cross-sections for excitations associated with spin-3/2
spin-tetramer configurations is determined. Comparison of magnetic
susceptibility and inelastic neutron scattering results shows that the proposed
"lozenge" model is not distinctly supported, but provides evidence that the
system may be better described as a pair of non-interacting inequivalent
dimers, \textit{i.e} double dimers. However, the existence of long-range
magnetic order below $T_c \approx 28$ K immediately questions such a
description. Although no evidence of the lozenge model is observed, future
studies on single crystals may further clarify the appropriate magnetic
Hamiltonian.
