  The gas-to-dust ratio of reddened stars in the Milky Way (MW), the Magellanic
Clouds, and in general is usually expressed as a linear relation between the
hydrogen column density, N(H), and the reddening, E(B-V), or extinction in the
V band (A(V)). If the extinction curve was truly universal, the strength of the
relationship and the linearity would naturally be maintained for extinction at
any wavelength, and also for N(H) vs. E(B-V). However, extinction curves vary
within the Milky Way, and there is no reason why, except by chance, either
E(B-V) or A(V) would be the most physical measure of dust column density. In
this paper, we utilize for the first time full extinction curves to 41 MW
sightlines and find that the scatter between N(H) and extinction is minimized
-- and the relation becomes linear -- for extinction at 2900 +/- 160 A. Scatter
and nonlinearity increase at longer wavelengths and are especially large for
near-IR extinction. We conclude that near-UV extinction is a superior measure
of the dust column density for MW dust. We provide new, non-linear gas-to-dust
relations for various dust tracers. We also find that the very large
discrepancy between MW and SMC gas-to-dust ratios of 0.9 dex in N(H)/E(B-V) is
reduced to 0.7 dex for far-UV extinction, which matches the difference in
cosmic abundances of carbon between the two galaxies, and therefore confirms
that N(C) is the preferred measure of the gas in the gas-to-dust ratio, even
though it may not be a convenient one.
