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Technological advances in radio telescopes and X-ray instruments over thelast 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 thesedistances 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 orrecalculate 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 surfacebrightness-to-diameter ($\Sigma-D$) relation. The slopes derived here ($\beta =-2.64$ including Cas A, $\beta = -2.38$ without Cas A) are significantlyflatter than those derived in previous studies. An independent test of theaccuracy of the $\Sigma-D$ relation was performed by using the extragalacticSNRs in the Large and Small Magellanic Clouds. The limitations of the$\Sigma-D$ relation and the assumptions necessary for its use are discussed. Arevised Galactic distribution of SNRs is presented based on the reviseddistances as well as those calculated from this $\Sigma-D$ relation. A scalingmethod is employed to compensate for observational selection effects bycomputing scale factors based on individual telescope survey sensitivities,angular resolutions and sky coverage. The radial distribution of the surfacedensity of shell SNRs, corrected for selection effects, is presented andcompared to previous works.Comment: 26 pages, 7 figures, uses aaspp4.sty, to appear in ApJ (Sept. 10

A New Σ‐DRelation and Its Application to the Galactic Supernova Remnant Distribution