  We present a table of 215 SNRs with distances. New distances are found to SNR
G$51.26+0.11$ of $6.6 \pm 1.7$ kpc using HI absorption spectra, and to 5 other
SNRs using maser/molecular cloud associations. We recalculate the distances and
errors to all SNRs using a consistent rotation curve and provide errors where
they were not previously estimated. This results in a significant distance
revisions for 20 SNRs. Because of observational constraints and selection
effects, there to be is an apparent deficit of observed number of Galactic
supernova remnants (SNRs). To investigate this, we employ two methods. The
first method applies correction factors for the selection effects to derive the
radial density distribution. The second method compares functional forms for
the SNR surface density and selection function against the data to find which
functions are consistent with the data. The total number of SNRs in the Galaxy
is $\sim3500$ (Method 1) or in the range $\sim2400$ to $\sim5600$ (Method 2).
We conclude that the current observed number of SNRs is not yet complete enough
to give a well-determined total SNR number or radial density function.
