  Combined HERA data on charm production in deep-inelastic scattering have
previously been used to determine the charm-quark running mass $m_c(m_c)$ in
the MSbar renormalisation scheme. Here, the same data are used as a function of
the photon virtuality $Q^2$ to evaluate the charm-quark running mass at
different scales to one-loop order, in the context of a next-to-leading order
QCD analysis. The scale dependence of the mass is found to be consistent with
QCD expectations.
