  The incompressible liquid-drop (ILD) model reproduces masses of stable nuclei
rather well. Here we show how the ILD volume, surface, symmetry, and Coulomb
energies are related to the equation of state of nuclear matter using the
Oyamatsu-Iida (OI) macroscopic nuclear model, which has reasonable many-body
energy and isoscalar inhomogeneity gradient energy. We use 304 update
interactions, covering wide ranges of the incompressibility $K_0$ of symmetric
matter and the density slope of symmetry energy $L$, which fit almost equally
empirical mass and radius data of stable nuclei. Thus, the $K_0$ and $L$
dependences are nearly frozen in stable nuclei as in the ILD model, leading to
clear correlations among interaction and saturation parameters. Furthermore, we
assume that the surface energy of the OI model is twice as large as the
gradient energy using the size equilibrium conditions of the ILD and OI models.
Then, the four energies of the ILD and OI models agree well for stable nuclei
with $A \gtrsim 40$. Meanwhile, the OI model with $L \lesssim 100$ MeV predicts
the latest mass data better than those of stable nuclei, and we suggest $20
\lesssim L \lesssim 90$ MeV, although the lower boundary is not constrained
well.
