The measured line profiles of the Si iv3s ${\mathrm{}}^{2}$S--3p ${\mathrm{}}^{2}$P\ifmmode^\circ\else\textdegree\fi{} doublet during 10-T operation on the Alcator-C tokamak show evidence of a contribution due to the Zeeman effect to these profiles. The assumption that these line profiles are single lines broadened only by instrumental effects and thermal broadening yields apparent kinetic temperatures for the two lines which differ by approximately 50%. Neither of the resulting temperatures is reasonable for Si iv under typical Alcator operating conditions and the difference between the temperatures cannot be explained by Doppler effects. Modifying the nonlinear least-squares fitting routine to include the (unresolved) components predicted by the weak-field limit of the Zeeman effect yields kinetic temperatures for these lines which are in agreement and are reasonable for the region of the plasma in which Si iv exists. Finally, a study of the Zeeman effect in O vii shows that contributions from this process are important in determining ion temperatures from line broadening of the O vii 2s ${\mathrm{}\mathrm{}}^{3}$${\mathrm{S}}_{1}$--2p ${\mathrm{}}^{3}$P\ifmmode^\circ\else\textdegree\fi{}${\mathrm{}}_{2}$ emission line in the vuv spectrum from Alcator-C plasmas.