  We examine relations among the parameters characterizing the phenomenological
equation of state (EOS) of nearly symmetric, uniform nuclear matter near the
saturation density by comparing macroscopic calculations of radii and masses of
stable nuclei with the experimental data. The EOS parameters of interest here
are the symmetry energy S_0, the symmetry energy density-derivative coefficient
L and the incompressibility K_0 at the normal nuclear density. We find a
constraint on the relation between K_0 and L from the empirically allowed
values of the slope of the saturation line (the line joining the saturation
points of nuclear matter at finite neutron excess), together with a strong
correlation between S_0 and L. In the light of the uncertainties in the values
of K_0 and L, we macroscopically calculate radii of unstable nuclei as expected
to be produced in future facilities. We find that the matter radii depend
strongly on L while being almost independent of K_0, a feature that will help
to determine the L value via systematic measurements of nuclear size.
