THE ASTRONOMICAL JOURNAL VOLUME 109, NUMBER 3, PAGE 1086 MARCH 1995 A PHOTOMETRIC STUDY OF THE GLOBULAR CLUSTER M54 AND THE SAGITTARIUS DWARF GALAXY: EVIDENCE FOR THREE DISTINCT POPULATIONS ATA SARAJEDINI Kitt Peak National Observatory, National Optical Astronomy Observatories, P.O. Box 26732, Tucson, Arizona 85726 Electronic mail: ata@noao.edu ANDREW C. LAYDEN Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatories, Casilla 603, La Serena, Chile Electronic mail: alayden@noao.edu ABSTRACT We present VI CCD color-magnitude diagrams for the globular cluster M54 and the Sagittarius dwarf galaxy. These are used to derive the following quantities: [Fe/H] = -1.79 +/- 0.08 for M54 and [Fe/H] = -0.52 +/- 0.09 for Sagittarius. We find a metallicity dispersion of +/- 0.16 dex in M54, and we infer the possible existence of a [Fe/H] ~ -1.3 component in Sagittarius, which may have a metallicity dispersion as well. The mean reddening in the direction of M54 is E(B-V) = 0.13 +/- 0.02. The distances to M54 and Sagittarius, determined using their horizontal branch magnitudes, are identical to within the uncertainties of existing RR Lyrae luminosity-abundance relations. This, together with positional and radial velocity arguments, suggests that M54 is physically associated with Sagittarius. We note that M54 is substantially brighter than the globular cluster members of the Fornax dwarf spheroidal galaxy, and that the metal abundance of Sagittarius is quite high for its estimated absolute magnitude.