  We report new observations of ZnII and CrII absorption lines in 10 damped
\lya systems (DLAs), mostly at redshift $z_{abs} \simgt 2.5$ . By combining
these results with those from our earlier survey (Pettini et al. 1994) and
other recent data, we construct a sample of 34 measurements (or upper limits)
of the Zn abundance relative to hydrogen [Zn/H]; the sample includes more than
one third of the total number of DLAs known.
  The plot of the abundance of Zn as a function of redshift reinforces the two
main findings of our previous study. (1) Damped \lya systems are mostly
metal-poor, at all redshifts sampled; the column density weighted mean for the
whole data set is [Zn/H] $= -1.13 \pm 0.38$ (on a logarithmic scale), or
approximately 1/13 of solar. (2) There is a large spread, by up to two orders
of magnitude, in the metallicities we measure at essentially the same
redshifts. We propose that damped \lya systems are drawn from a varied
population of galaxies of different morphological types and at different stages
of chemical evolution, supporting the idea of a protracted epoch of galaxy
formation.
  At redshifts $z \simgt 2$ the typical metallicity of the damped \lya systems
is in agreement with expectations based on the consumption of HI gas implied by
the recent measurements of $\Omega_{DLA}$ by Storrie-Lombardi et al. (1996a),
and with the metal ejection rates in the universe at these epochs deduced by
Madau (1996) from the ultraviolet luminosities of high redshift galaxies
revealed by deep imaging surveys. There are indications in our data for an
increase in the mean metallicity of the damped \lya systems from $z > 3$ to
$\approx 2$, consistent with the rise in the comoving star formation rate
indicated by the relative numbers of $U$ and $B$ drop-outs in the Hubble Deep
Field. Although such comparisons are still tentative, it appears that these
different avenues for exploring the early evolution of galaxies give a broadly
consistent picture.
