  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.
