The recent Hubble Space Telescope (HST) observations of the z(q) = 3.2
86 quasar Q0302-003 (Jakobeen et al. 1994) and the z(q) = 3.185 quasar
Q1935-67 by Tytler (1995) show absorption edges at the redshifted wav
elength of He II 304 Angstrom. A key goal is to distinguish between co
ntributions from discrete Ly alpha forest clouds and a smoothly distri
buted intergalactic medium (IGM). We model the contributions from each
of these sources of He II absorption, including the distribution of l
ine Doppler widths and column densities, the ''He II proximity effect'
' from the quasar, and a self-consistent derivation of the He Il opaci
ty of the universe as a function of the spectrum of ionizing sources,
with the assumption that both the clouds and the IGM are photoionized.
The He II edge can be fully accounted for by He II line blanketing fo
r reasonable distributions of line widths and column densities in the
Ly alpha forest, provided that the ionizing sources have spectral inde
x alpha(s) > 1.5, and any He II proximity effect is neglected. Even wi
th some contribution from a diffuse IGM, it is difficult to account fo
r the edge observed by Jakobsen et al. (1994) with a ''hard'' source s
pectrum (alpha(s), < 1.3). The proximity effect modifies the relative
contributions of the clouds and IGM to tau(HeII), near the quasar (z l
ess than or similar to z(q)) and markedly increases the amount of He I
I absorption required. This implies, for example, that to account for
the He II edge with line blanketing alone, the minimum spectral index
a(s) must be increased from 1.5 to 1.9. We demonstrate the need for hi
gher resolution observations that characterize the change in transmiss
ion as z --> z(q) and resolve line-free gaps in the continuum. We set
limits on the density of the diffuse IGM and suggest that the IGM and
Ly alpha clouds are likely to be a significant repository for dark bar
yons.