A search for distant X-ray galaxy clusters

. We report on the progress of our search for serendipitous distant X-ray galaxy clusters in the ROSAT PSPC pointed observations archive. The initial aim of our work is to measure the X-ray luminosity function of clusters down to f lim = 4 \Theta 10 \Gamma14 erg cm \Gamma2 s \Gamma1 and so test the claims of cluster evolution at moderate redshifts. We have R band images and spectroscopy for 45 extended sources detected in 50 of the 100 deepest southern fields. A preliminary analysis suggests we cover a range of distances, from nearby clusters to possible distant clusters, z ' 1:0. 1. Introduction One of the major goals of cosmology is to probe the evolution of structure with lookback time. Galaxy clusters play a key role in this ambition because: -- Their formation by gravitational collapse is understood well enough to allow comparisons of observations with theoretical predictions of density evolution. -- They can be observed out to cosmologically significant distances (z ' 1:..