IRAM spectra of 34 radio sources

Binned in E_B-V_, N(H_2_) and N(DNM) are strongly correlated and vary by factors of 50=100 over the observed range E_B-V_~0.05-1mag, while N(HI) varies by factors of only 2-3. On average N(DNM) and N(H_2_) are well matched, and detecting HCO- absorption adds little to no H_2_ in excess of the previously inferred DNM. There are five cases where 2N(H_2_)<N(DNM)/2 indicates saturation of the HI emission profile.

For sightlines with W_CO_>=1K-km/s, the CO-H_2_ conversion factor N(H_2_)/W_CO_=2-3x10^20^cm^-2^/(1K-km/s) is higher than is derived from studies of resolved clouds in gamma-rays. Our work sampled primarily atomic gas with a mean H_2_ fraction ~1/3, but the DNM is almost entirely molecular. CO fulfills its role as an H_2_ tracer when its emission is strong, but large-scale CO surveys are not sensitive to H_2_ columns associated with typical values N(DNM)=2-6x10^20^cm^-2^.

Lower X_CO_ values from gamma-ray studies arise in part from different definitions and usage. Sightlines with W_CO_>=1K-km/s represent 2/3 of the H_2_ detected in HCO+ and detecting 90% of the H_2_ would require detecting CO at levels W_co_~=0.2-0.3K-km/s.