E(B-V), N(H I) and N(H_2)

We consider the structure of the N(H I) - E(B-V) relationship when H I is measured in the 21 cm radio line and \EBV\ is defined by far-IR dust-derived measures. We derive reddening-dependent corrections to N(H I) based on interferometric absorption measurements over the past 30 years that follow a single power-law relationship $\int \tau(H I) dv = 14.07 ~\kms\$\EBV$^{1.074}$ at 0.02 $\la$ \EBV\ $\la$ 3 mag. Corrections to 21cm line-derived H I column densities are too small to have had any effect on the ratio N(H I)/\EBV\ $= 8.3 \times 10^{21}\pcc$ mag$^{-1}$ we derived at 0.015 $\la$ \EBV\ $\la$ 0.075 mag and \absb\ $\ge$ 20\degr; they are also too small to explain the break in the slope of the N(H I) - \EBV\ relation at \EBV\ $\ga$ 0.1 mag that we demonstrated around the Galaxy at \absb $\ge 20$\degr. The latter must therefore be attributed to the onset of \HH-formation and we show that models of \HH\ formation in a low density diffuse molecular gas can readily explain the inflected N(H I)- \EBV\ relationship. Below \absb\ = 20\degr\ N(H I)/\EBV\ measured at 0.015 $\la$ \EBV\ $\la$ 0.075 mag increases steadily down to \absb\ = 8\degr\ where sightlines with small \EBV\ no longer occur. By contrast, the ratio N(H I)/\EBV\ measured over all \EBV\ declines to N(H I)/\EBV\ $= 5-6 \times 10^{21}\pcc$ mag$^{-1}$ at \absb\ $\la 30$\degr, perhaps providing an explanation of the difference between our results and the gas/reddening ratios measured previously using stellar spectra.