  Technological advances in radio telescopes and X-ray instruments over the
last 20 years have greatly increased the number of known supernova remnants
(SNRs) and led to a better determination of their properties. In particular,
more SNRs now have reasonably determined distances. However, many of these
distances were determined kinematically using old rotation curves (based on
$R_{\sun} = 10$ kpc and $V_{\sun} = 250$ km/s). A more modern rotation curve
(based on $R_{\sun} = 8.5$ kpc and $V_{\sun} = 220$ km/s) is used to verify or
recalculate the distances to these remnants. We use a sample of 36 shell SNRs
(37 including Cas A) with known distances to derive a new radio surface
brightness-to-diameter ($\Sigma-D$) relation. The slopes derived here ($\beta =
-2.64$ including Cas A, $\beta = -2.38$ without Cas A) are significantly
flatter than those derived in previous studies. An independent test of the
accuracy of the $\Sigma-D$ relation was performed by using the extragalactic
SNRs in the Large and Small Magellanic Clouds. The limitations of the
$\Sigma-D$ relation and the assumptions necessary for its use are discussed. A
revised Galactic distribution of SNRs is presented based on the revised
distances as well as those calculated from this $\Sigma-D$ relation. A scaling
method is employed to compensate for observational selection effects by
computing scale factors based on individual telescope survey sensitivities,
angular resolutions and sky coverage. The radial distribution of the surface
density of shell SNRs, corrected for selection effects, is presented and
compared to previous works.
