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We are currently investigating the possibility that clusters of galaxies may not be evolved objects which are dynamically relaxed but may be currently forming via mergers of groups and poor clusters. Optical studies of clusters have provided evidence of a clumpy galaxy distribution in clusters, which would support the merger hypothosis. However, much of the controversy about the significance of substructure in clusters can be traced to the use of galaxies as test particles in the optical studies. In many cases the number of galaxies identified in the suspected substructure is too few to eliminate statistical uncertainty in the identification. We are searching for substructure in clusters of galaxies using X-ray images of clusters, because the sensitivity of the X-ray gas to small variations of the potential makes these observations a powerful tool to search for substructure which avoids many of the problems with an optical search. We have fit the 2-d surface brighness for all clusters in the Edge et al. (1990) flux-limited sample of clusters with imaging data. This includes both Einstein IPC images along with ROSAT PSPC data. We find that $\sim$30\% of the clusters have isolated structure in the X-ray data. We are currently identifing structure in the X-ray images with optical identifications of substructure from Bird (1993) to correlate the X-ray structure with optical structure. The combined X-ray and optical information will allow us to determine the size and mass of the objects merging with the clusters. Once we have determined the fraction of our sample with substructure we can then compare our observations with current theory and numerical models of cluster formation.
