as tr o - ph / 9 40 50 03 2 M ay 1 99 4 Damped

Although the Cold + Hot Dark Matter (CHDM) cosmology provides perhaps the best t of any model to all the available data at the current epoch, CHDM produces structure at relatively low redshifts and thus could be ruled out if there were evidence for formation of massive objects at high redshifts. Damped Ly systems are abundant in quasar absorption spectra and thus provide possibly the most signiicant evidence for early structure formation, and thus perhaps the most stringent constraint on CHDM. Using the numbers of halos in N-body simulations to normalize Press-Schechter estimates of the number densities of protogalaxies as a function of redshift, we nd that CHDM with c = = b = 0:6=0:3=0:1 is compatible with the damped Ly data at 2:5, but that it is probably incompatible with the limited z > 3 damped Ly data. The situation is uncertain because there is very little data for z > 3, and also it is unclear whether all damped Ly systems are associated with collapsed protogalaxies. The predictions of CHDM are quite sensitive to the hot (neutrino) fraction, and we nd that c = = b = 0:675=0:25=0:075 is compatible even with the z > 3 data. This corresponds to lowering the neutrino mass from 6.8 to 5.7 eV, for H 0 = 50 km s 1 Mpc 1. In CHDM, the higher redshift damped Ly systems are predicted to have lower masses, which can be checked by measuring the velocity widths of the associated metal line systems.