We present detailed observations of the 1.2 mm continuum and the CO li
ne emission in the exceptional starburst/active galaxy NGC 3079 with t
he IRAM 30-m telescope. The 1.2 mm thermal dust emission is much less
centrally concentrated than the CO or radio continuum. Roughly 10% of
the total 1.2 mm flux comes from the central 11 '' as opposed to simil
ar to 40% for the CO or radio continuum. We find no evidence for cool
dust in the center of NGC 3079. A dust temperature of 32 K fits the da
ta well. We then determine N(H-2)ICO(2-1) approximate to 3 X 10(19) cm
(-2) (K km s(-1))(-1), roughly an order of magnitude below most estima
tes. In the disk, cool dust is present. For T-dust = 17 K, the cross-s
ection (or absorption coefficient) we derive for dust in the atomic me
dium is very close to the value of Draine & Lee (1984). The combinatio
n of the errors in the HI column density and the 1.2 mm thermal dust e
mission are probably less than a factor 2 in these and other recent ob
servations. Unless the dust temperature has been severely overestimate
d, the dependence of the dust opacity on wavelength (lambda) is closer
to lambda(-2) than lambda(-1.5) between 100 mu m and 1.2 mm.Based on
this cross-section, we estimate an average conversion factor of N(H-2)
/ICO(2-1) approximate to 1 - 2 X 10(20) cm(-2)(K km s(-1))(-1) in the
disk. This is within the range of estimates for our galactic disk, alt
hough lower than early estimates. Given the very low N(H-2)/ICO(2-1) v
alue found for the nuclear region, we compare it with ratios derived f
rom radiative transfer equations and (CO)-C-13 measurements. These est
imates are in good agreement with our dust-based N(H-2)/ICO(2-1) facto
r. It appears unlikely that grain emission is enhanced (with respect t
o that in the atomic medium) through grain-grain agglomeration or thro
ugh condensation of molecules onto grains. The dust mantles may be par
tially evaporated in the center of NGC 3079. The dust temperature may
allow evaporation of CO-rich mantles and C-shocks are another plausibl
e mechanism capable of disrupting mantles while leaving CO molecules i
ntact. The effect would be to raise the N(H-2)/ICO(2-1) ratio slightly
and to increase the gas-phase CO abundance.