  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.
