  Surface photometry from 16 HST/WFPC2 fields in the I(F814W) filter is used to
derive the distribution of apparent axis ratios for galaxies in progressively
fainter magnitude intervals for I<25. We assess the systematic and accidental
errors in ellipticity measurements as a function of image resolution and
signal-to-noise ratio, and statistically correct for the effect of cosmological
surface brightness dimming on our isophotal measurements. The axis ratio
distribution for the local galaxy population was computed using logR
measurements for 1569 RC3 galaxies with Bt<13 mag. Nonparametric tests are used
to show that our distant samples, in the redshift range 0.1<z<1.5, are not
statistically different from the local sample. We present image montages of
galaxies selected randomly from different axis ratio and apparent magnitude
ranges and discuss the evolutionary consequences of the lack of a strong
difference between the ellipticity distributions in near and far data sets.
