AN INTERCOMPARISON AMONG STAR CATALOGS .4. AN EXTENSION OF THE THEORY

In this paper we extend the development of the theory of star catalog examination, coordinate mean error evaluation, and proper motion mean error assessment introduced in the first paper of this series. Specifi cally, we have now shown how to compare positions of a star in differe nt catalogs rather than just coordinates. Thus, the enlarged theory is intrinsically two-dimensional. Further extensions are conceptually st raightforward and should have many applications to comparable catalog- to-catalog homogenization and systematic error elimination in multicol or photometric work. In two dimensions, the special case of equal coor dinate errors leads to the Rayleigh distribution for the prediction of the angular distance apart distribution. This prediction is tested us ing all the catalogs examined in Paper III and using the Southern Refe rence Star (SRS) program source catalogs against a recompilation of th e SRS completed in 1993. The conclusions regarding the relative superi ority of the large-scale star catalogs, which were the focus of Paper III, are borne out by the new testing. There is, however, a confusing result: the southern hemisphere tests are always superior to the north ern ones. Also, the anomalous AGK3 findings, for a catalog without sta tistical adjustment in any meaningful sense, is explained.