  We present a detailed study of an estimator of the HI column density, based
on a combination of HI 21cm absorption and HI 21cm emission spectroscopy. This
"isothermal" estimate is given by $N_{\rm HI,ISO} = 1.823 \times 10^{18} \int
\left[ \tau_{\rm tot} \times {\rm T_B} \right] / \left[ 1 - e^{-\tau_{\rm tot}}
\right] {\rm dV}$, where $\tau_{\rm tot}$ is the total HI 21cm optical depth
along the sightline and ${\rm T_B}$ is the measured brightness temperature. We
have used a Monte Carlo simulation to quantify the accuracy of the isothermal
estimate by comparing the derived $N_{\rm HI,ISO}$ with the true HI column
density $N_{\rm HI}$. The simulation was carried out for a wide range of
sightlines, including gas in different temperature phases and random locations
along the path. We find that the results are statistically insensitive to the
assumed gas temperature distribution and the positions of different phases
along the line of sight. The median value of the ratio of the true H{\sc i}
column density to the isothermal estimate, $N_{\rm HI}/{N_{\rm HI, ISO}}$, is
within a factor of 2 of unity while the 68.2% confidence intervals are within a
factor of $\approx 3$ of unity, out to high HI column densities, $\le 5 \times
10^{23}$\,cm$^{-2}$ per 1 km s$^{-1}$ channel, and high total optical depths,
$\le 1000$. The isothermal estimator thus provides a significantly better
measure of the HI column density than other methods, within a factor of a few
of the true value even at the highest columns, and should allow us to directly
probe the existence of high HI column density gas in the Milky Way.
