We present a modification of the theoretical ? ? D relation for supernova remnants (SNRs) in the adiabatic expansion phase. This modification is based on the convolution of the relation first derived by Shklovsky with the ? ? D relation derived in this paper for thermal bremsstrahlung radiation from the ionized gas cloud. We adopt McKee & Ostriker?s model for the components of the interstellar medium as part of our derivation. The modified Shklovsky theory agrees well with empirical results. Kesteven?s modified theoretical relation gives the best agreement with the updated Galactic empirical ? ? D relation.
