  Analyzing three approximate methods to locate liquid-solid coexistence in
simple systems, an observation is made that all of them predict the same
functional dependence of the temperature on density at freezing and melting of
the conventional Lennard-Jones system. The emerging equations can be written as
$T={\mathcal A}\rho^4+{\mathcal B}\rho^2$ in normalized units. We suggest to
determine the values of the coefficients ${\mathcal A}$ at freezing and melting
from the high-temperature limit, governed by the inverse twelfth power
repulsive potential. The coefficients ${\mathcal B}$ can be determined from the
triple point parameters of the LJ fluid. This produces freezing and melting
equations which are exact in the high-temperature limit and at the triple
point, and show remarkably good agreement with numerical simulation data in the
intermediate region.
