Scattering effects have always been an important systematic problem in absorption measurements. A new integrating cavity absorption meter has been developed that, in principle, is rigorously independent of scattering effects. The theoretical basis for this integrating cavity device is developed and applied to a generic experimental device: a one-dimensional model is described that demonstrates qualitatively the observed deviations from ideal; details of an actual device are provided; and experimental results for the absorption coefficient of aqueous solutions with various absorptions and with various concentrations of scatterers are presented.