We have obtained optical recombination-line abundances for the third-row element magnesium in ten planetary nebulae. The nebulae in our sample include four (NGC 7009, NGC 6153, M 2–36 and M 1–42) for which we have previously found very large enhancements, relative to solar, in the recombination line abundances of the second-row elements carbon, nitrogen, oxygen and neon (Liu et al. 1995, Liu et al. 2000, Liu et al. 2001). Nebular temperature fluctuations appear unable to account for these effects. However, models that invoke high-density clumps, particularly clumps which are hydrogen-deficient, appear more viable as an explanation for the high recombination line abundances that are observed (see Liu et al. 2000 for more details). While it may be possible to appeal to astrophysical nucleosynthetic processes to enhance the CNONe second-row elements in AGB stars, such effects are not expected to modify the abundances of third-row elements such as magnesium. We have therefore measured and dereddened the intensities of the 4481 Å 4f-3d line of Mg II, relative to Hβ, in order to investigate whether magnesium recombination line abundances are enhanced or not.