  We present a theory of the melting of elemental solids as a
dislocation-mediated phase transition. We model dislocations near melt as
non-interacting closed strings on a lattice. In this framework we derive simple
expressions for the melting temperature and latent heat of fusion that depend
on the dislocation density at melt. We use experimental data for more than half
the elements in the Periodic Table to determine the dislocation density from
both relations. Melting temperatures yield a dislocation density of (0.61\pm
0.20) b^{-2}, in good agreement with the density obtained from latent heats,
(0.66\pm 0.11) b^{-2}, where b is the length of the smallest
perfect-dislocation Burgers vector. Melting corresponds to the situation where,
on average, half of the atoms are within a dislocation core.
