E(B - V), N(H I), AND N(H2)

We consider the structure of the N(H I)-E(B - V) relationship when Hi is measured in the 21 cm radio line and E(B - V) 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 yr that follow a single power-law relationship integral tau(H I)d v = 14.07 km s(-1) E(B - V)(1.074) at 0.02 less than or similar to E(B - V) less than or similar to 3 mag. Corrections to 21 cm line-derived H I column densities are too small to have had any effect on the ratio N(H I)/E(B - V) = 8.3 x 10(21) cm(-2) mag(-1) we derived at 0.015 less than or similar to E(B - V) less than or similar to 0.075 mag and |b| >= 20 degrees; they are also too small to explain the break in the slope of the N(H I)-E(B - V) relation at E(B - V) greater than or similar to 0.1 mag that we demonstrated around the Galaxy at |b| >= 20 degrees. The latter must therefore be attributed to the onset of H-2 formation and we show that models of H-2 formation in a low-density diffuse molecular gas can readily explain the inflected N (H I)-E(B-V) relationship. Below |b| = 20 degrees N(H I)/E(B-V) measured at 0.015 less than or similar to E(B - V) less than or similar to 0.075 mag increases steadily down to |b| = 8 degrees where sightlines with small E(B - V) no longer occur. By contrast, the ratio N(H I)/E(B - V) measured over all E(B - V) declines to N(H I)/E(B - V) = 5-6 x 10(21) cm(-2) mag(-1) at |b| less than or similar to 30 degrees, perhaps providing an explanation of the difference between our results and the gas/reddening ratios measured previously using stellar spectra.