Optical Reddening, Integrated HI Optical Depth, Total Hydrogen Column Density

Despite the vastly different angular scales on which they are measured, the integrated $\lambda$21 cm \HI\ optical depth measured interferometrically, \WHI, is a good proxy for the optical reddening derived from IR dust emission, with %\WHI\ $\equiv \int\tau({\rm \HI}) ~{\rm dv} = (13.8\pm0.7)$\EBV$^{(1.10\pm0.03)}$ \kms\ \WHI\ $\propto$ \EBV$^{1.10}$ for 0.04 mag $\la$ \EBV\ $\la$ 4 mag. For \EBV\ $\la 0.04$ mag or \WHI\ $< 0.7$ \kms, less-absorbent warm and ionized gases assert themselves and $\tau$(HI) is a less reliable tracer of \EBV. The \WHI-\EBV\ relationship can be inverted to give a broken power-law relationship between the total hydrogen column density N(H) and \WHI\ such that knowledge of \WHI\ alone predicts N(H) with an accuracy of a factor 1.5 ($\pm 0.18$ dex) across two orders of magnitude variation of \WHI. The \WHI-N(H) relation is invariant under a linear rescaling of the reddening measure used in the analysis and does not depend on knowing properties of the HI such as the spin temperature.