We present a table of 215 SNRs with distances. %estimate New distances are
found to SNR G$51.26+0.11$ of $6.6\pm 1.7$ kpc using HI absorption
spectra%Additionally, 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 %seems 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 $\sim 3500$
(Method 1) or in the range $\sim 2400$ to $\sim 5600$ (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.