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VRI photometric observations of surface-brightness fluctuation in 13 Virgo Cluster galaxies, M32, and NGC 3379, obtained using an 800 x 800 CCD array on the 4-m telescope at KPNO during March 1989, are reported. The data-reduction techniques are described in detail, and the results are presented in tables and graphs. Particular attention is given to distance estimates derived from the I-band fluctuations: it is shown that NGC 4365 is behind the cluster, while NGC 4468 and NGC 4489 are in the foreground. The average distance to the cluster is found to be 17 + or - 1 Mpc, with H0 = 78 + or - 6 km/sec Mpc; the corresponding values from a direct isochrone calibration are 21 Mpc and 64 + or - 5 km/sec Mpc.

A relatively direct technique of determining extragalactic distances is described. The method relies on measuring the luminosity fluctuations that arise from the counting statistics of the stars contributing the flux in each pixel of a high signal-to-noise CCD image of a galaxy. The amplitude of these fluctuations is inversely proportional to the distance of the galaxy. This approach bypasses most of the successive stages of calibration required in the traditional extragalactic distance ladder; the only serious drawback to this method is that it requires an accurate knowledge of the bright end of the luminosity function. Potentially, this method can produce accurate distances of elliptical galaxies and spiral bulges at distances out to about 20 Mpc. In this paper, it is explained how to calculate the value of the fluctuations, taking into account various sources of contamination and the effects of finite spatial resolution, and the feasibility and limitations of this technique are demonstrated via simulations and CCD images of M 32 and N 3379.