We present the first high spectral resolution X-ray observation of the giant elliptical galaxy NGC 4636 , obtained with the Reflection Grating Spectrometer on-board the XMM-Newton Observatory . The resulting spectrum contains a wealth of emission lines from various charge states of oxygen , neon , magnesium , and iron . Examination of the cross-dispersion profiles of several of these lines provides clear , unambiguous evidence of resonance scattering by the highest oscillator strength lines , as well as a weak temperature gradient in the inner regions of the interstellar medium . We invoke a sophisticated new Monte Carlo technique which allows us to properly account for these effects in performing quantitative fits to the spectrum . Our spectral fits are not subject to many of the systematics that have plagued earlier investigations . The derived metal abundances are higher than have been inferred from prior , lower spectral resolution observations of this source ( Awaki et al . 1994 ) , but are still incompatible with conventional chemical enrichment models of elliptical galaxies . In addition , our data are incompatible with standard cooling flow models for this system - our derived upper limit to the mass deposition rate is below the predicted value by a factor of 3–5 .