  Neutrons stars lighter than the Sun are basically composed of nuclear matter
of density up to around twice normal nuclear density. In our recent analyses,
we showed that possible simultaneous observations of masses and radii of such
neutron stars could constrain $\eta\equiv(K_0L^2)^{1/3}$, a combination of the
incompressibility of symmetric nuclear matter $K_0$ and the density derivative
of the nuclear symmetry energy $L$ that characterizes the theoretical
mass-radius relation. In this paper, we focus on the mass-radius constraint of
the X-ray burster 4U 1724-307 given by Suleimanov et al. (2011). We therefrom
obtain the constraint that $\eta$ should be larger than around 130 MeV, which
in turn leads to $L$ larger than around 110, 98, 89, and 78 MeV for $K_0=180$,
230, 280, and 360 MeV. Such a constraint on $L$ is more or less consistent with
that obtained from the frequencies of quasi-periodic oscillations in giant
flares observed in soft-gamma repeaters.
