The total secondary-electron yield from thin carbon foils traversed by heavy ions has been measured as a function of the projectile atomic number ${\mathit{Z}}_{\mathit{p}}$, the initial charge state, and the incident velocity. For nearly all projectiles in the velocity region studied the number of emitted electrons per incoming projectile \ensuremath{\gamma} and the stopping power S have, as expected, the same velocity dependence. However, for ions with ${\mathit{Z}}_{\mathit{p}}$g29 a slight increase of the ratio \ensuremath{\Lambda}=\ensuremath{\gamma}/S with the projectile energy is observed. A systematic study of the ratio \ensuremath{\Lambda} as a function of the projectile atomic number ${\mathit{Z}}_{\mathit{p}}$ indicates a ${\mathit{Z}}_{\mathit{p}}^{\mathrm{\ensuremath{-}}0.2}$ dependence of the parameter \ensuremath{\Lambda}. Possible explanations for this ${\mathit{Z}}_{\mathit{p}}^{\mathrm{\ensuremath{-}}0.2}$ dependence of the \ensuremath{\Lambda} parameter are given.