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 .