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 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 years that follow a single power-law relationship \int \tau ( HI ) dv = 14.07 ~ { } \mbox { km s$ { } ^ { -1 } $ } E ( B-V ) ^ { 1.074 } at 0.02 \lesssim E ( B-V ) \lesssim 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 ) /E ( B-V ) = 8.3 \times 10 ^ { 21 } \mbox { $ { ~ { } { cm } ^ { -2 } } $ } mag ^ { -1 } we derived at 0.015 \lesssim E ( B-V ) \lesssim 0.075 mag and |b| \geq 20 ^ { o } ; 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 ) \gtrsim 0.1 mag that we demonstrated around the Galaxy at |b| \geq 20 ^ { o } .
The latter must therefore be attributed to the onset of \mathrm { H _ { 2 } } -formation and we show that models of \mathrm { 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 ^ { o } N ( H I ) /E ( B-V ) measured at 0.015 \lesssim E ( B-V ) \lesssim 0.075 mag increases steadily down to |b| = 8 ^ { o } 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 \times 10 ^ { 21 } \mbox { $ { ~ { } { cm } ^ { -2 } } $ } mag ^ { -1 } at |b| \lesssim 30 ^ { o } , perhaps providing an explanation of the difference between our results and the gas/reddening ratios measured previously using stellar spectra .