Two basic formulas for resonance absorption applicable both to mixtures and to lumps are considered, the narrow resonance (NR) approximation and the infinite mass (NRIA) approximation. The formulas are shown to be complementary, yielding accurate results when the choice between them is based on the practical width of the resonance line as originally suggested by Wigner. The formulas are used to calculate resonance integrals for U238 and Th232. The results yield a low mass absorption term and a surface absorption term proportional to the square root of the surface-to-mass ratio for lumps of practical size in qualitative agreement with the experimental work of Egiazarov and Hellstrand for U238 and with Dayton and Pettus for thorium. Dresner’s suggestion that the ratio of the resonance integral to the mass absorption term is independent of the resonance structure is not borne out. Refinement of the basic formulas is discussed. The correction of the NRIA formula for energy degradation is in agreement with Spinney’s calculations for U-H mixtures and with Monte Carlo results obtained by Auerbach for uranium-water lattices. Consideration of lumping effects indicates that the basic formulas generally underestimate the resonance absorption. It is therefore recommended that the common use of ill-defined flux disadvantage factors be dropped.