Distances measured using Cepheid variable stars have been essential for establishing the cosmological distance scale and the value of the Hubble constant. These stars have remained the primary extragalactic distance indicator since 1929 because of the small observed scatter in the relationship between their pulsation period and luminosity, their large numbers, which allow many independent measures of the distance to a galaxy, and the simplicity of the basic physics underlying their variability. Potential systematic uncertainties in the use of the LMC-calibrated Cepheid period-luminosity relation to determine distances using HST are estimated to be 8-10%. Here we describe the results of a search for Cepheids in the nearby galaxy NGC 4258, which has an independently determined geometric distance of 7.2 +/- 0.5 Mpc (Herrnstein et al. 1999). We obtain a Cepheid distance of 8.1 +/- 0.4 (excluding possible systematic errors affecting all HST Cepheid distances) Mpc; there is a 1.3 sigma difference between the two measurements. If the maser-based distance is adopted and other HST Cepheid distances are revised according to our results, the derived value of the Hubble constant would be increased by 12 +/- 9%, and the corresponding age of the Universe would decrease by the same factor.
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