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A photometric survey of faint galaxies in three high Galactic latitude fields(each $\sim49~\rm{arcmin^{2}}$) with sub-arcsecond seeing is used to study theclustering properties of the faint galaxy population. Multi-color photometry ofthe galaxies has been obtained to magnitude limits of $V\sim25$, $R\sim25$ and$I\sim24$. Angular correlation analysis is applied to magnitude-limited andcolor-selected samples of galaxies from the three fields for angularseparations ranging from $10-126''$. General agreement is obtained with otherrecent studies which show that the amplitude of the angular correlationfunction, $\omega(\theta)$, is smoothly decreasing as a function of limitingmagnitude. The observed decline of $\omega(\theta)$ rules out the viability of``maximal merger'' galaxy evolution models. Using redshift distributionsextrapolated to faint magnitude limits, models of galaxy clustering evolutionare calculated and compared to the observed I-band $\omega(\theta)$. Faintgalaxies are determined to have correlation lengths and clustering evolutionparameters of either $r_{0}\sim4~h^{-1}~Mpc$ and $\epsilon\sim0-1$;$r_{0}\sim5-6~h^{-1}~Mpc$ and $\epsilon>1$; or $r_{0}\sim2-3~h^{-1}~ Mpc$ and$\epsilon\sim-1.2$, assuming $q_{0}=0.5$ and with $h=H_{0}/100~km~s^{-1}~Mpc^{-1}$. The latter case is for clustering fixed in co-movingcoordinates and is probably unrealistic since most local galaxies are observedto be more strongly clustered. No significant variations in the clusteringamplitude as a function of color are detected, for all the color-selectedgalaxy samples considered. (Abridged)Comment: LaTeX (aaspp4.sty), 54 pages including 15 postscript figures; 3  additional uuencoded, gzipped postscript files (~300 kb each) of Figs. 1, 2  and 3 available at ftp://ftp.astro.ubc.ca/pub/woods ; To be published in the  Nov. 20, 1997 issue of The Astrophysical Journa

Measuring the Angular Correlation Function for Faint Galaxies in High Galactic Latitude Fields