We present a new survey for damped Ly alpha systems with redshifts z a
pproximate to 1.6-3.0. The survey is based on a sample of 228 QSOs dra
wn from the Large Bright QSO Survey (LBQS). We find a total of 20 cand
idate damped Ly alpha lines with rest frame equivalent widths determin
ed from low-resolution spectroscopy of W greater than or equal to 10 A
ngstrom. Using intermediate-resolution spectroscopy, we and other work
ers confirm 12 of these candidates and an additional candidate with W
< 10 Angstrom as damped Ly alpha systems with H I column densities N(H
I) greater than or equal to 2 x 10(20) cm(-2). All the systems were d
rawn from a redshift path Delta z = 121.0 along which it is possible t
o detect damped Ly alpha candidates with W greater than or equal to 5
Angstrom at 5 sigma statistical significance. We combine the results o
f the LBQS damped survey with results of previous surveys for damped s
ystems to form a ''statistical sample'' of 62 damped Ly alpha systems
with N(H I) greater than or equal to 2 x 10(20) cm(-2). These systems
are drawn from a total redshift path Delta z = 323.8. A list of 18 add
itional damped Ly alpha systems not found in systematic surveys is als
o presented. Therefore, we are aware of 80 damped Ly alpha absorption
systems at the time of writing (1995 March) with N(H I) greater than o
r equal to 2 x 10(20) cm(-2). The following is a summary of results ba
sed on the ''statistical sample. 1. The LBQS damped survey increases t
he sensitivity for finding damped Ly alpha systems in the redshift int
erval z approximate to 1.6-2.5. 2. Using the ''statistical sample,'' w
e find that the quantity n(z), the number of absorbers per unit redshi
ft interval with N(H I) greater than or equal to 2 x 10(20) cm(-2) sho
ws no evidence for intrinsic evolution. The new n(z) exhibits little s
catter around a systematic increase of n(z) with z and is in excellent
agreement with our previous determination of n(z). 3. Our determinati
on of Omega(g)(z), the comoving mass density of neutral gas at redshif
t z, shows a monotonically increasing form of Omega(g)(z) with z for t
he first time. The new data support and strengthen the earlier conclus
ion that the comoving density of neutral gas increases with redshift.
Comparison of n(z) for systems having N(H I) greater than or equal to
2 x 10(20) cm(-2) with a subset having N(H I) greater than or equal to
10(21) cm(-2) shows the decrease of Omega(g) with time to arise from
the decline of the high column density systems. 4. We determine f(hr,
z), the frequency distribution of H I column densities. The new f(N, z
) shows considerably less scatter than was present in the previous res
ult, especially in the highest redshift bin z = 2.5-3.5, where f(N, z)
is now well represented by a single N-1 power law. The new f(N, z) sh
ows the decline of the high column density systems with time explicitl
y. 5. We interpret the evolution of Omega(g)(z) to result from gas con
sumption by star formation. The principal arguments are as follows: (a
) there is good agreement between Omega(g) in the highest redshift bin
and Omega(star), the density of visible matter in nearby galaxies, (b
) Omega(g)(z) decreases monotonically with decreasing z and approaches
the neutral gas density determined from 21 cm emission by nearby gala
xies at z = 0, (c) gas consumption by star formation in nearby spirals
increases rapidly with increasing N(H I), which is consistent with ou
r finding that the high column density systems disappear with time, an
d (d) detailed investigations of individual objects reveal gas that is
quiescent, cold, and possibly in a state of rotation; i.e., the type
of gas in which stars are known to form. 6. We present a new model for
the evolution of f(N, z). The model incorporates star formation in ra
ndomly oriented exponential disks. The star formation rates are consis
tent with the Schmidt-Kennicutt expressions for star formation. The mo
del predictions are in good agreement with the data. 7. Comparison bet
ween the neutral gas content of damped Ly alpha systems with the baryo
nic density predicted by big bang nucleosynthesis shows the damped sys
tems at high z to contain at least 10% of the baryonic content of the
universe. All the evidence cited above supports the idea that the damp
ed Ly alpha systems are the progenitors of current galaxies.