  Relativistic and non-relativistic ratios of Laplace transform QCD moment sum
rules for charmonium are used in order to determine the value of the on-shell
charm-quark mass. The validity of the non-relativistic version of QCD sum rules
in this particular application is discussed. After using current values of the
perturbative and non-perturbative QCD parameters, as well as experimental data
on the $J/\psi$ system, we obtain $m_{c}(Q^{2}=m_{c}^{2}) = 1.46 \pm 0.07
\;\mbox{GeV}$.
