The Hubble Space Telescope is being used to measure accurate Cepheid distances to nearby galaxies with the ultimate aim of determining the Hubble constant, H_0. For the first time, it has become feasible to use Cepheid variables to derive a distance to a galaxy in the southern hemisphere cluster of Fornax. Based on the discovery of 37 Cepheids in the Fornax galaxy NGC 1365, a distance to this galaxy of 18.6 +/- 0.6 Mpc (statistical error only) is obtained. This distance leads to a value of H_0 = 70 +/- 7 (random) +/- 18 (systematic) km/sec/Mpc in good agreement with estimates of the Hubble constant further afield.
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