Integral experiments have been conducted to study rethermalization in moderating media having temperature discontinuities. Neutron absorption rates of Cu63, Au197, and Lu176 have been observed near these discontinuities in the temperatures of concentric annuli of graphite and of water and graphite systems. For this report the data have been analyzed with a two-thermal-group diffusion model of the space and energy distribution of the thermal neutrons. Cross sections and relaxation distances for neutron rethermalization in water and graphite have been inferred from the analyses. These rethermalization cross sections are integral representations of the scattering kernel. The relaxation distances were found to be shorter for the rethermalization of cold neutrons in warm graphite than for the rethermalization of warm neutrons in cold graphite. The cross section of hot graphite for rethermalization of 300°K neutrons increases monotonically to near the free gas value, 0.0614 cm−1, as the graphite temperature increases to 850°K. The cross section of 300°K graphite for rethermalization of 850°K neutrons is well below the free gas value, in agreement with theoretical calculations. Within the limits of the heavy gas model one can define an effective mass in terms of the rethermalization cross section. Effective masses of graphite reported here are comparable with those inferred by others from lattice-spectrum measurements. The rethermalization cross sections of 300°K water presented here yield effective masses of the water molecule that lie in the range of 4.1 to 7.2 amu for 410 to 720°K neutrons, respectively.