passes through POS1. The number of M31 stars we see in POS2 consequently underestimates the number we would expect to find in POS1. From interpolation of blue M31 isophotes plotted by Hodge & Kennicutt (1982) and by deVaucouleurs (1958) and from color-index data by Walterbos & Kennicutt (1988), we estimate the [*V*]{} surface brightness gradient of M31 in the vicinity of M32 to be approximately 0.0035 mag/arcsec. From this we conclude that the stellar surface density expected at POS1 is 1.2 times that found at POS2.

Completeness tests were carried out by adding $\approx 500$ artificial stars, with colors and magnitudes selected from grid points in the CM diagram, to each of the POS1 F555W and F814W images. The pixel locations of the added stars were randomly chosen and identical between F555W and F814W frames. The frames were then processed using DAOPHOT II and ALLFRAME in a manner identical to that applied to the original data. The results of these tests are shown in Figures \[fig:compfig\] and \[fig:returned\], which show that the 50% completeness level for most POS1 stars occurs at $I\approx 24.9$ and $V\approx25.4.$ Virtually identical tests were carried out for POS2.

The M32 CM diagram was corrected for 