Using deep Hubble Space Telescope imaging, color-magnitude diagrams are constructed for the globular clusters 47 Tuc and NGC 6397. As expected, because of its lower metal abundance, the main sequence of NGC 6397 lies well to the blue of that of 47 Tuc. A comparison of the white dwarf cooling sequences of the two clusters, however, demonstrates that these sequences are indistinguishable over most of their loci - a consequence of the settling out of heavy elements in the dense white dwarf atmosphere and the near equality of their masses. Lower quality data on M4 continues this trend to a third cluster whose metallicity is intermediate between these two. While the path of the white dwarfs in the color-magnitude diagram is nearly identical in 47 Tuc and NGC 6397, the numbers of white dwarfs along the path are not. This results from the relatively rapid relaxation in NGC 6397 compared to 47 Tuc and provides a cautionary note that simply counting objects in star clusters in random locations as a method of testing stellar evolutionary theory is likely dangerous unless dynamical considerations are included.
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